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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Influenza Infectious Dose May Explain the High Mortality of the Second and Third Wave of 1918–1919 Influenza Pandemic</title><author><name sortKey="Paulo, A Cristina" sort="Paulo, A Cristina" uniqKey="Paulo A" first="A. Cristina" last="Paulo">A. Cristina Paulo</name><affiliation><nlm:aff id="aff1"><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Correia Neves, Margarida" sort="Correia Neves, Margarida" uniqKey="Correia Neves M" first="Margarida" last="Correia-Neves">Margarida Correia-Neves</name><affiliation><nlm:aff id="aff1"><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Domingos, Tiago" sort="Domingos, Tiago" uniqKey="Domingos T" first="Tiago" last="Domingos">Tiago Domingos</name><affiliation><nlm:aff id="aff2"><addr-line>Environment and Energy Scientific Area, DEM, and IN+, Center for Innovation Technology and Research, Instituto Superior Técnico, Lisboa, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Murta, Alberto G" sort="Murta, Alberto G" uniqKey="Murta A" first="Alberto G." last="Murta">Alberto G. Murta</name><affiliation><nlm:aff id="aff3"><addr-line>Instituto Nacional dos Recursos Biolgicos - IPIMAR, Lisboa, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Pedrosa, Jorge" sort="Pedrosa, Jorge" uniqKey="Pedrosa J" first="Jorge" last="Pedrosa">Jorge Pedrosa</name><affiliation><nlm:aff id="aff1"><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">20668679</idno><idno type="pmc">2909907</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2909907</idno><idno type="RBID">PMC:2909907</idno><idno type="doi">10.1371/journal.pone.0011655</idno><date when="2010">2010</date><idno type="wicri:Area/Pmc/Corpus">000B13</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000B13</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Influenza Infectious Dose May Explain the High Mortality of the Second and Third Wave of 1918–1919 Influenza Pandemic</title><author><name sortKey="Paulo, A Cristina" sort="Paulo, A Cristina" uniqKey="Paulo A" first="A. Cristina" last="Paulo">A. Cristina Paulo</name><affiliation><nlm:aff id="aff1"><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Correia Neves, Margarida" sort="Correia Neves, Margarida" uniqKey="Correia Neves M" first="Margarida" last="Correia-Neves">Margarida Correia-Neves</name><affiliation><nlm:aff id="aff1"><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Domingos, Tiago" sort="Domingos, Tiago" uniqKey="Domingos T" first="Tiago" last="Domingos">Tiago Domingos</name><affiliation><nlm:aff id="aff2"><addr-line>Environment and Energy Scientific Area, DEM, and IN+, Center for Innovation Technology and Research, Instituto Superior Técnico, Lisboa, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Murta, Alberto G" sort="Murta, Alberto G" uniqKey="Murta A" first="Alberto G." last="Murta">Alberto G. Murta</name><affiliation><nlm:aff id="aff3"><addr-line>Instituto Nacional dos Recursos Biolgicos - IPIMAR, Lisboa, Portugal</addr-line></nlm:aff></affiliation></author><author><name sortKey="Pedrosa, Jorge" sort="Pedrosa, Jorge" uniqKey="Pedrosa J" first="Jorge" last="Pedrosa">Jorge Pedrosa</name><affiliation><nlm:aff id="aff1"><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></nlm:aff></affiliation></author></analytic><series><title level="j">PLoS ONE</title><idno type="eISSN">1932-6203</idno><imprint><date when="2010">2010</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><sec><title>Background</title><p>It is widely accepted that the shift in case-fatality rate between waves during the 1918 influenza pandemic was due to a genetic change in the virus. In animal models, the infectious dose of influenza A virus was associated to the severity of disease which lead us to propose a new hypothesis. We propose that the increase in the case-fatality rate can be explained by the dynamics of disease and by a dose-dependent response mediated by the number of simultaneous contacts a susceptible person has with infectious ones.</p></sec><sec><title>Methods</title><p>We used a compartment model with seasonality, waning of immunity and a Holling type II function, to model simultaneous contacts between a susceptible person and infectious ones. In the model, infected persons having mild or severe illness depend both on the proportion of infectious persons in the population and on the level of simultaneous contacts between a susceptible and infectious persons. We further allowed for a high or low rate of waning immunity and volunteer isolation at different times of the epidemic.</p></sec><sec><title>Results</title><p>In all scenarios, case-fatality rate was low during the first wave (Spring) due to a decrease in the effective reproduction number. The case-fatality rate in the second wave (Autumn) depended on the ratio between the number of severe cases to the number of mild cases since, for each 1000 mild infections only 4 deaths occurred whereas for 1000 severe infections there were 20 deaths. A third wave (late Winter) was dependent on the rate for waning immunity or on the introduction of new susceptible persons in the community. If a group of persons became voluntarily isolated and returned to the community some days latter, new waves occurred. For a fixed number of infected persons the overall case-fatality rate decreased as the number of waves increased. This is explained by the lower proportion of infectious individuals in each wave that prevented an increase in the number of severe infections and thus of the case-fatality rate.</p></sec><sec><title>Conclusion</title><p>The increase on the proportion of infectious persons as a proxy for the increase of the infectious dose a susceptible person is exposed, as the epidemic develops, can explain the shift in case-fatality rate between waves during the 1918 influenza pandemic.</p></sec></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Potter, Cw" uniqKey="Potter C">CW Potter</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kilbourne, Ed" uniqKey="Kilbourne E">ED Kilbourne</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ansart, S" uniqKey="Ansart S">S Ansart</name></author><author><name sortKey="Pelat, C" uniqKey="Pelat C">C Pelat</name></author><author><name sortKey="Boelle, Py" uniqKey="Boelle P">PY Boelle</name></author><author><name sortKey="Carrat, F" uniqKey="Carrat F">F Carrat</name></author><author><name sortKey="Flahault, A" uniqKey="Flahault A">A Flahault</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Miller, Ma" uniqKey="Miller M">MA Miller</name></author><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author><author><name sortKey="Balinska, M" uniqKey="Balinska M">M Balinska</name></author><author><name sortKey="Simonsen, L" uniqKey="Simonsen L">L Simonsen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Taubenberger, Jk" uniqKey="Taubenberger J">JK Taubenberger</name></author><author><name sortKey="Morens, D" uniqKey="Morens D">D Morens</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Murray, Cjl" uniqKey="Murray C">CJL Murray</name></author><author><name sortKey="Lopez, Ad" uniqKey="Lopez A">AD Lopez</name></author><author><name sortKey="Chin, B" uniqKey="Chin B">B Chin</name></author><author><name sortKey="Feehan, D" uniqKey="Feehan D">D Feehan</name></author><author><name sortKey="Hill, Kh" uniqKey="Hill K">KH Hill</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Payne, Amm" uniqKey="Payne A">AMM Payne</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author><author><name sortKey="Grais, Rf" uniqKey="Grais R">RF Grais</name></author><author><name sortKey="Lafont, Bap" uniqKey="Lafont B">BAP Lafont</name></author><author><name sortKey="Miller, Ma" uniqKey="Miller M">MA Miller</name></author><author><name sortKey="Simonsen, L" uniqKey="Simonsen L">L Simonsen</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Kobasa, D" uniqKey="Kobasa D">D Kobasa</name></author><author><name sortKey="Takada, A" uniqKey="Takada A">A Takada</name></author><author><name sortKey="Shinya, K" uniqKey="Shinya K">K Shinya</name></author><author><name sortKey="Hatta, M" uniqKey="Hatta M">M Hatta</name></author><author><name sortKey="Halfmann, P" uniqKey="Halfmann P">P Halfmann</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Tumpey, Tm" uniqKey="Tumpey T">TM Tumpey</name></author><author><name sortKey="Garcia Sastre, A" uniqKey="Garcia Sastre A">A Garcia-Sastre</name></author><author><name sortKey="Taubenberger, Jk" uniqKey="Taubenberger J">JK Taubenberger</name></author><author><name sortKey="Palese, P" uniqKey="Palese P">P Palese</name></author><author><name sortKey="Swayne, De" uniqKey="Swayne D">DE Swayne</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kobasa, D" uniqKey="Kobasa D">D Kobasa</name></author><author><name sortKey="Jones, Sm" uniqKey="Jones S">SM Jones</name></author><author><name sortKey="Shinya, K" uniqKey="Shinya K">K Shinya</name></author><author><name sortKey="Kash, Jc" uniqKey="Kash J">JC Kash</name></author><author><name sortKey="Copps, J" uniqKey="Copps J">J Copps</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Morens, Dm" uniqKey="Morens D">DM Morens</name></author><author><name sortKey="Taubenberger, Jk" uniqKey="Taubenberger J">JK Taubenberger</name></author><author><name sortKey="Fauci, As" uniqKey="Fauci A">AS Fauci</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Klugman, Kp" uniqKey="Klugman K">KP Klugman</name></author><author><name sortKey="Astley, M" uniqKey="Astley M">M Astley</name></author><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M Lipsitch</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Gibbs, Mj" uniqKey="Gibbs M">MJ Gibbs</name></author><author><name sortKey="Armstrong, Js" uniqKey="Armstrong J">JS Armstrong</name></author><author><name sortKey="Gibbs, Aj" uniqKey="Gibbs A">AJ Gibbs</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Enserink, M" uniqKey="Enserink M">M Enserink</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Tumpey, Tm" uniqKey="Tumpey T">TM Tumpey</name></author><author><name sortKey="Maines, Tr" uniqKey="Maines T">TR Maines</name></author><author><name sortKey="Hoeven, Nv" uniqKey="Hoeven N">NV Hoeven</name></author><author><name sortKey="Glaser, L" uniqKey="Glaser L">L Glaser</name></author><author><name sortKey="Sol Rzano, A" uniqKey="Sol Rzano A">A Solórzano</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Taubenberger, Jk" uniqKey="Taubenberger J">JK Taubenberger</name></author><author><name sortKey="Reid, Ah" uniqKey="Reid A">AH Reid</name></author><author><name sortKey="Janczewski, Ta" uniqKey="Janczewski T">TA Janczewski</name></author><author><name sortKey="Fanning, Tg" uniqKey="Fanning T">TG Fanning</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Reid, Ah" uniqKey="Reid A">AH Reid</name></author><author><name sortKey="Janczewski, Ta" uniqKey="Janczewski T">TA Janczewski</name></author><author><name sortKey="Lorens, Rm" uniqKey="Lorens R">RM Lorens</name></author><author><name sortKey="J, Ea" uniqKey="J E">EA J</name></author><author><name sortKey="Daniels, Rs" uniqKey="Daniels R">RS Daniels</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Oxford, Js" uniqKey="Oxford J">JS Oxford</name></author><author><name sortKey="Lambkin, R" uniqKey="Lambkin R">R Lambkin</name></author><author><name sortKey="Sefton, A" uniqKey="Sefton A">A Sefton</name></author><author><name sortKey="Daniels, R" uniqKey="Daniels R">R Daniels</name></author><author><name sortKey="Elliot, A" uniqKey="Elliot A">A Elliot</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Oxford, Js" uniqKey="Oxford J">JS Oxford</name></author><author><name sortKey="Sefton, A" uniqKey="Sefton A">A Sefton</name></author><author><name sortKey="Jackson, R" uniqKey="Jackson R">R Jackson</name></author><author><name sortKey="Innes, W" uniqKey="Innes W">W Innes</name></author><author><name sortKey="Daniels, Rs" uniqKey="Daniels R">RS Daniels</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Markel, H" uniqKey="Markel H">H Markel</name></author><author><name sortKey="Lipman, Hb" uniqKey="Lipman H">HB Lipman</name></author><author><name sortKey="Navarro, Ja" uniqKey="Navarro J">JA Navarro</name></author><author><name sortKey="Sloan, A" uniqKey="Sloan A">A Sloan</name></author><author><name sortKey="Michalsen, Jr" uniqKey="Michalsen J">JR Michalsen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kawana, A" uniqKey="Kawana A">A Kawana</name></author><author><name sortKey="Naka, G" uniqKey="Naka G">G Naka</name></author><author><name sortKey="Fujikura, Y" uniqKey="Fujikura Y">Y Fujikura</name></author><author><name sortKey="Kato, Y" uniqKey="Kato Y">Y Kato</name></author><author><name sortKey="Mizuno, Y" uniqKey="Mizuno Y">Y Mizuno</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Barry, Jm" uniqKey="Barry J">JM Barry</name></author><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author><author><name sortKey="Simonsen, L" uniqKey="Simonsen L">L Simonsen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mcsweeny, K" uniqKey="Mcsweeny K">K McSweeny</name></author><author><name sortKey="Colman, A" uniqKey="Colman A">A Colman</name></author><author><name sortKey="Fancourt, N" uniqKey="Fancourt N">N Fancourt</name></author><author><name sortKey="Parnell, M" uniqKey="Parnell M">M Parnell</name></author><author><name sortKey="Stantiall, S" uniqKey="Stantiall S">S Stantiall</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chowell, G" uniqKey="Chowell G">G Chowell</name></author><author><name sortKey="Bettencourt, Lma" uniqKey="Bettencourt L">LMA Bettencourt</name></author><author><name sortKey="Johnson, N" uniqKey="Johnson N">N Johnson</name></author><author><name sortKey="Alonso, Wj" uniqKey="Alonso W">WJ Alonso</name></author><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H Nishiura</name></author><author><name sortKey="Chowell, G" uniqKey="Chowell G">G Chowell</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mamelund, Se" uniqKey="Mamelund S">SE Mamelund</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Gottfredsson, M" uniqKey="Gottfredsson M">M Gottfredsson</name></author><author><name sortKey="Halldorsson, Bv" uniqKey="Halldorsson B">BV Halldorsson</name></author><author><name sortKey="Jonsson, S" uniqKey="Jonsson S">S Jonsson</name></author><author><name sortKey="Kristjansson, M" uniqKey="Kristjansson M">M Kristjansson</name></author><author><name sortKey="Kristjansson, K" uniqKey="Kristjansson K">K Kristjansson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Richard, Sa" uniqKey="Richard S">SA Richard</name></author><author><name sortKey="Sugaya, N" uniqKey="Sugaya N">N Sugaya</name></author><author><name sortKey="Simonsen, L" uniqKey="Simonsen L">L Simonsen</name></author><author><name sortKey="Miller, Ma" uniqKey="Miller M">MA Miller</name></author><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Francis, Byt" uniqKey="Francis B">BYT Francis</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Taylor, Rm" uniqKey="Taylor R">RM Taylor</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pinto, Ca" uniqKey="Pinto C">CA Pinto</name></author><author><name sortKey="Haff, Rf" uniqKey="Haff R">RF Haff</name></author><author><name sortKey="Stewart, Rc" uniqKey="Stewart R">RC Stewart</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Yetter, Ra" uniqKey="Yetter R">Ra Yetter</name></author><author><name sortKey="Lehrer, S" uniqKey="Lehrer S">S Lehrer</name></author><author><name sortKey="Ramphal, R" uniqKey="Ramphal R">R Ramphal</name></author><author><name sortKey="Small, Pa" uniqKey="Small P">PA Small</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Oh, S" uniqKey="Oh S">S Oh</name></author><author><name sortKey="Mccaffery, Jm" uniqKey="Mccaffery J">JM McCaffery</name></author><author><name sortKey="Eichelberger, Mc" uniqKey="Eichelberger M">MC Eichelberger</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wattrang, E" uniqKey="Wattrang E">E Wattrang</name></author><author><name sortKey="Jessett, Dm" uniqKey="Jessett D">DM Jessett</name></author><author><name sortKey="Yates, P" uniqKey="Yates P">P Yates</name></author><author><name sortKey="Fuxler, L" uniqKey="Fuxler L">L Fuxler</name></author><author><name sortKey="Hannant, D" uniqKey="Hannant D">D Hannant</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lu, H" uniqKey="Lu H">H Lu</name></author><author><name sortKey="Castro, Ae" uniqKey="Castro A">AE Castro</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ja, M" uniqKey="Ja M">M Ja</name></author><author><name sortKey="D, H" uniqKey="D H">H D</name></author><author><name sortKey="Dm, J" uniqKey="Dm J">J Dm</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Srivastava, B" uniqKey="Srivastava B">B Srivastava</name></author><author><name sortKey="Blazejewska, P" uniqKey="Blazejewska P">P Blazejewska</name></author><author><name sortKey="Hebmann, M" uniqKey="Hebmann M">M Hebmann</name></author><author><name sortKey="Bruder, D" uniqKey="Bruder D">D Bruder</name></author><author><name sortKey="Geffers, R" uniqKey="Geffers R">R Geffers</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Carrat, F" uniqKey="Carrat F">F Carrat</name></author><author><name sortKey="Vergu, E" uniqKey="Vergu E">E Vergu</name></author><author><name sortKey="Ferguson, Nm" uniqKey="Ferguson N">NM Ferguson</name></author><author><name sortKey="Lemaitre, M" uniqKey="Lemaitre M">M Lemaitre</name></author><author><name sortKey="Cauchemez, S" uniqKey="Cauchemez S">S Cauchemez</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hancioglu, B" uniqKey="Hancioglu B">B Hancioglu</name></author><author><name sortKey="Swigon, D" uniqKey="Swigon D">D Swigon</name></author><author><name sortKey="Clermont, G" uniqKey="Clermont G">G Clermont</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chang, Db" uniqKey="Chang D">DB Chang</name></author><author><name sortKey="Young, Cs" uniqKey="Young C">CS Young</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Brankston, G" uniqKey="Brankston G">G Brankston</name></author><author><name sortKey="Gitterman, L" uniqKey="Gitterman L">L Gitterman</name></author><author><name sortKey="Hirji, Z" uniqKey="Hirji Z">Z Hirji</name></author><author><name sortKey="Lemieux, C" uniqKey="Lemieux C">C Lemieux</name></author><author><name sortKey="Gardan, M" uniqKey="Gardan M">M Gardan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Tellier, R" uniqKey="Tellier R">R Tellier</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nicas, M" uniqKey="Nicas M">M Nicas</name></author><author><name sortKey="Best, D" uniqKey="Best D">D Best</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mathews, Jd" uniqKey="Mathews J">JD Mathews</name></author><author><name sortKey="Mccaw, Ct" uniqKey="Mccaw C">CT Mccaw</name></author><author><name sortKey="Mcvernon, J" uniqKey="Mcvernon J">J Mcvernon</name></author><author><name sortKey="Mcbryde, Es" uniqKey="Mcbryde E">ES Mcbryde</name></author><author><name sortKey="Mccaw, Jm" uniqKey="Mccaw J">JM Mccaw</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ferguson, Nm" uniqKey="Ferguson N">NM Ferguson</name></author><author><name sortKey="Cummings, Dat" uniqKey="Cummings D">DAT Cummings</name></author><author><name sortKey="Fraser, C" uniqKey="Fraser C">C Fraser</name></author><author><name sortKey="Cajka, Jc" uniqKey="Cajka J">JC Cajka</name></author><author><name sortKey="Cooley, Pc" uniqKey="Cooley P">PC Cooley</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Halloran, Me" uniqKey="Halloran M">ME Halloran</name></author><author><name sortKey="Ferguson, Nm" uniqKey="Ferguson N">NM Ferguson</name></author><author><name sortKey="Eubank, S" uniqKey="Eubank S">S Eubank</name></author><author><name sortKey="Longini, Im" uniqKey="Longini I">IM Longini</name></author><author><name sortKey="Cummings, Dat" uniqKey="Cummings D">DAT Cummings</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Andreasen, V" uniqKey="Andreasen V">V Andreasen</name></author><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author><author><name sortKey="Simonsen, L" uniqKey="Simonsen L">L Simonsen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Davies, Jr" uniqKey="Davies J">JR Davies</name></author><author><name sortKey="Grilli, Ea" uniqKey="Grilli E">EA Grilli</name></author><author><name sortKey="Smith, Aj" uniqKey="Smith A">AJ Smith</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Grilli, Ea" uniqKey="Grilli E">EA Grilli</name></author><author><name sortKey="Davies, Jr" uniqKey="Davies J">JR Davies</name></author><author><name sortKey="Smith, Aj" uniqKey="Smith A">AJ Smith</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sonoguchi, T" uniqKey="Sonoguchi T">T Sonoguchi</name></author><author><name sortKey="Sakoh, M" uniqKey="Sakoh M">M Sakoh</name></author><author><name sortKey="Kunita, N" uniqKey="Kunita N">N Kunita</name></author><author><name sortKey="Satsuta, K" uniqKey="Satsuta K">K Satsuta</name></author><author><name sortKey="Fukumi, H" uniqKey="Fukumi H">H Fukumi</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Renshaw, E" uniqKey="Renshaw E">E Renshaw</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Weber, Tp" uniqKey="Weber T">TP Weber</name></author><author><name sortKey="Stilianakis, Ni" uniqKey="Stilianakis N">NI Stilianakis</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Shaman, J" uniqKey="Shaman J">J Shaman</name></author><author><name sortKey="Kohn, M" uniqKey="Kohn M">M Kohn</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M Lipsitch</name></author><author><name sortKey="Viboud, C" uniqKey="Viboud C">C Viboud</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Vynnycky, E" uniqKey="Vynnycky E">E Vynnycky</name></author><author><name sortKey="Edmunds, Wj" uniqKey="Edmunds W">WJ Edmunds</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dushoff, J" uniqKey="Dushoff J">J Dushoff</name></author><author><name sortKey="Plotkin, Jb" uniqKey="Plotkin J">JB Plotkin</name></author><author><name sortKey="Levin, Sa" uniqKey="Levin S">SA Levin</name></author><author><name sortKey="Earn, Djd" uniqKey="Earn D">DJD Earn</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mills, Ce" uniqKey="Mills C">CE Mills</name></author><author><name sortKey="Robins, Jm" uniqKey="Robins J">JM Robins</name></author><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M Lipsitch</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="White, Lf" uniqKey="White L">LF White</name></author><author><name sortKey="Pagano, M" uniqKey="Pagano M">M Pagano</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">PLoS One</journal-id><journal-id journal-id-type="iso-abbrev">PLoS ONE</journal-id><journal-id journal-id-type="publisher-id">plos</journal-id><journal-id journal-id-type="pmc">plosone</journal-id><journal-title-group><journal-title>PLoS ONE</journal-title></journal-title-group><issn pub-type="epub">1932-6203</issn><publisher><publisher-name>Public Library of Science</publisher-name><publisher-loc>San Francisco, USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">20668679</article-id><article-id pub-id-type="pmc">2909907</article-id><article-id pub-id-type="publisher-id">10-PONE-RA-15905R1</article-id><article-id pub-id-type="doi">10.1371/journal.pone.0011655</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="Discipline"><subject>Mathematics/Mathematical Computing</subject><subject>Infectious Diseases/Respiratory Infections</subject><subject>Public Health and Epidemiology/Infectious Diseases</subject></subj-group></article-categories><title-group><article-title>Influenza Infectious Dose May Explain the High Mortality of the Second and Third Wave of 1918–1919 Influenza Pandemic</article-title><alt-title alt-title-type="running-head">Pandemic Influenza Mortality</alt-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Paulo</surname><given-names>A. Cristina</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib><contrib contrib-type="author"><name><surname>Correia-Neves</surname><given-names>Margarida</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Domingos</surname><given-names>Tiago</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Murta</surname><given-names>Alberto G.</given-names></name><xref ref-type="aff" rid="aff3"><sup>3</sup></xref></contrib><contrib contrib-type="author"><name><surname>Pedrosa</surname><given-names>Jorge</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>Life and Health Sciences Research Institute, School of Health Sciences, Universidade do Minho, Braga, Portugal</addr-line></aff><aff id="aff2"><label>2</label><addr-line>Environment and Energy Scientific Area, DEM, and IN+, Center for Innovation Technology and Research, Instituto Superior Técnico, Lisboa, Portugal</addr-line></aff><aff id="aff3"><label>3</label><addr-line>Instituto Nacional dos Recursos Biolgicos - IPIMAR, Lisboa, Portugal</addr-line></aff><contrib-group><contrib contrib-type="editor"><name><surname>Belshaw</surname><given-names>Robert</given-names></name><role>Editor</role><xref ref-type="aff" rid="edit1"></xref></contrib></contrib-group><aff id="edit1">University of Oxford, United Kingdom</aff><author-notes><corresp id="cor1">* E-mail: <email>cristinapaulo@ecsaude.uminho.pt</email></corresp><fn fn-type="con"><p>Conceived and designed the experiments: ACP TD AGM. Performed the experiments: ACP. Analyzed the data: ACP AGM. Wrote the paper: ACP MCN TD AGM JP.</p></fn></author-notes><pub-date pub-type="collection"><year>2010</year></pub-date><pub-date pub-type="epub"><day>26</day><month>7</month><year>2010</year></pub-date><volume>5</volume><issue>7</issue><elocation-id>e11655</elocation-id><history><date date-type="received"><day>27</day><month>1</month><year>2010</year></date><date date-type="accepted"><day>7</day><month>6</month><year>2010</year></date></history><permissions><copyright-statement>Paulo et al.</copyright-statement><copyright-year>2010</copyright-year><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><license-p>This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.</license-p></license></permissions><abstract><sec><title>Background</title><p>It is widely accepted that the shift in case-fatality rate between waves during the 1918 influenza pandemic was due to a genetic change in the virus. In animal models, the infectious dose of influenza A virus was associated to the severity of disease which lead us to propose a new hypothesis. We propose that the increase in the case-fatality rate can be explained by the dynamics of disease and by a dose-dependent response mediated by the number of simultaneous contacts a susceptible person has with infectious ones.</p></sec><sec><title>Methods</title><p>We used a compartment model with seasonality, waning of immunity and a Holling type II function, to model simultaneous contacts between a susceptible person and infectious ones. In the model, infected persons having mild or severe illness depend both on the proportion of infectious persons in the population and on the level of simultaneous contacts between a susceptible and infectious persons. We further allowed for a high or low rate of waning immunity and volunteer isolation at different times of the epidemic.</p></sec><sec><title>Results</title><p>In all scenarios, case-fatality rate was low during the first wave (Spring) due to a decrease in the effective reproduction number. The case-fatality rate in the second wave (Autumn) depended on the ratio between the number of severe cases to the number of mild cases since, for each 1000 mild infections only 4 deaths occurred whereas for 1000 severe infections there were 20 deaths. A third wave (late Winter) was dependent on the rate for waning immunity or on the introduction of new susceptible persons in the community. If a group of persons became voluntarily isolated and returned to the community some days latter, new waves occurred. For a fixed number of infected persons the overall case-fatality rate decreased as the number of waves increased. This is explained by the lower proportion of infectious individuals in each wave that prevented an increase in the number of severe infections and thus of the case-fatality rate.</p></sec><sec><title>Conclusion</title><p>The increase on the proportion of infectious persons as a proxy for the increase of the infectious dose a susceptible person is exposed, as the epidemic develops, can explain the shift in case-fatality rate between waves during the 1918 influenza pandemic.</p></sec></abstract><counts><page-count count="8"></page-count></counts></article-meta></front><body><sec id="s1"><title>Introduction</title><p>During the 20th century there were three influenza pandemics <xref rid="pone.0011655-Potter1" ref-type="bibr">[1]</xref>, <xref rid="pone.0011655-Kilbourne1" ref-type="bibr">[2]</xref> characterised by the occurrence, within one year of, at least, two to three successive epidemic waves and by an increase in the case-fatality rate in the later waves <xref rid="pone.0011655-Ansart1" ref-type="bibr">[3]</xref>, <xref rid="pone.0011655-Miller1" ref-type="bibr">[4]</xref>. The 1918 influenza pandemic caused up to 40 million deaths <xref rid="pone.0011655-Potter1" ref-type="bibr">[1]</xref>, <xref rid="pone.0011655-Taubenberger1" ref-type="bibr">[5]</xref>, <xref rid="pone.0011655-Murray1" ref-type="bibr">[6]</xref>, a number that far exceeded the number of fatalities in the 1957 and 1968 influenza pandemics, of about 2 and 1 million deaths, respectively <xref rid="pone.0011655-Payne1" ref-type="bibr">[7]</xref>–<xref rid="pone.0011655-World1" ref-type="bibr">[9]</xref>. The reasons behind the exceptionally high case-fatality rate in the 1918 influenza pandemic have been associated to the virus pathogenesis <xref rid="pone.0011655-Kobasa1" ref-type="bibr">[10]</xref>–<xref rid="pone.0011655-Kobasa2" ref-type="bibr">[12]</xref>, the absence of antibiotics to treat secondary bacteremia infections <xref rid="pone.0011655-Morens1" ref-type="bibr">[13]</xref>, <xref rid="pone.0011655-Klugman1" ref-type="bibr">[14]</xref> and to a debilitated health care system, exhausted by a frail population found at the end of World War I <xref rid="pone.0011655-Ansart1" ref-type="bibr">[3]</xref>. The increase in the case-fatality rate between waves, on the other hand, is attributed to the emergence of a pathogenic virus type after a genetic change in the circulating virus <xref rid="pone.0011655-Kobasa1" ref-type="bibr">[10]</xref> or to a reassortment with a zoonotic influenza virus <xref rid="pone.0011655-Gibbs1" ref-type="bibr">[15]</xref>–<xref rid="pone.0011655-Tumpey2" ref-type="bibr">[17]</xref>. The precise time at which the new virus type emerged is not known and at least two hypothesis have been proposed <xref rid="pone.0011655-Potter1" ref-type="bibr">[1]</xref>. Some authors advocate that the virus emerged immediately before the Autumn wave <xref rid="pone.0011655-Gibbs1" ref-type="bibr">[15]</xref>, <xref rid="pone.0011655-Taubenberger2" ref-type="bibr">[18]</xref>, whereas others proposed that the virus had seeded itself earlier in 1916 <xref rid="pone.0011655-Reid1" ref-type="bibr">[19]</xref>, <xref rid="pone.0011655-Oxford1" ref-type="bibr">[20]</xref>. Supporting the latter hypothesis is the small time interval of six months between the first and second wave for the new virus to spread worldwide, and the increase in the number of deaths from influenza-like illness in military camps and in small civilian communities during the winters of 1916 and 1917 <xref rid="pone.0011655-Oxford2" ref-type="bibr">[21]</xref>. Furthermore, the rate of evolution of the neuraminidase and hemagglutinin genes, whose coded proteins are determinant in the entry and exit of the virus in the host cell, suggest a possible emergence in 1915–1916 <xref rid="pone.0011655-Reid1" ref-type="bibr">[19]</xref>. The protracted period of almost two years, between seeding of the virus and the emergence of the 1918 influenza pandemic, was explained by the restricted travel during World War I which allowed the virus to maintain itself in small civilian communities and in army camps while increasing in virulence <xref rid="pone.0011655-Oxford1" ref-type="bibr">[20]</xref>, <xref rid="pone.0011655-Oxford2" ref-type="bibr">[21]</xref>. Later on, demobilisation of troops would have aided the spread of the virus worldwide <xref rid="pone.0011655-Oxford1" ref-type="bibr">[20]</xref>. However, this may not be the reason for the shift in disease severity, given that demobilisation started after the armistice signed in November 11th, that is, after the deadly second wave had peak in most European countries <xref rid="pone.0011655-Ansart1" ref-type="bibr">[3]</xref> and in many USA cities <xref rid="pone.0011655-Markel1" ref-type="bibr">[22]</xref>.</p><p>In this paper we explore a new hypothesis for the pattern of increased case-fatality rate during the latest waves of the 1918 influenza pandemic. This hypothesis is based on a dose-dependent response according to which influenza mortality increased when healthy susceptible persons were exposed to a high infectious dose of the 1918 influenza virus. The possibility of a dose-dependent response to explain the increased case-fatality rate during the second wave of the 1918 influenza pandemic has never been put forward. This is particularly surprising given the observation, in the laboratory setting, that only inoculation with a median infectious lethal dose, that is the dose that kill 50% of the animals inoculated, in mice <xref rid="pone.0011655-Kobasa1" ref-type="bibr">[10]</xref>, <xref rid="pone.0011655-Tumpey1" ref-type="bibr">[11]</xref> and in cynomolgus macaque model <xref rid="pone.0011655-Kobasa2" ref-type="bibr">[12]</xref>, caused extensive oedema and haemorrhagic exudates as reported for patients who succumbed to the 1918 influenza pandemic <xref rid="pone.0011655-Kobasa2" ref-type="bibr">[12]</xref>.</p><p>In this paper we used mathematical modelling to simulate the dynamics of influenza virus infection in an immunological naïve population, from invasion of the virus until one year later. To model the infectious dose we assumed that, in average, the dose is mediated by the number of simultaneous contacts a susceptible person has with infectious ones. We further distinguished between mild and severe disease by assuming a lower or a higher mortality rate, respectively.</p></sec><sec id="s2"><title>Results</title><p>Simulations from the proposed model showed a two-wave pattern and an increase on the case-fatality rate (CFR) during the second wave (<xref ref-type="fig" rid="pone-0011655-g001">Figure 1</xref>). This increase results from an increase in the incidence of severe cases that build up as the proportion of infectious persons in the population increases. The CFR for severe disease is 5 times higher then the CFR for mild disease, such that an increase of 1000 mild cases add to mortality 4 deaths whereas 1000 severe cases add to mortality 20 deaths. The increase in the CFR is also higher when the parameter that measures simultaneous contacts is higher, <inline-formula><inline-graphic xlink:href="pone.0011655.e001.jpg" mimetype="image"></inline-graphic></inline-formula> (<xref ref-type="fig" rid="pone-0011655-g001">Figure 1B</xref>). During the second wave there is a distinct mortality rate that depends on the infectious dose, here mediated by the number of simultaneous contacts, whereas for the first wave the mortality in both scenarios is almost the same (<xref ref-type="fig" rid="pone-0011655-g001">Figure 1</xref>). The first epidemic wave peaked in July, when the effective reproduction number (<inline-formula><inline-graphic xlink:href="pone.0011655.e002.jpg" mimetype="image"></inline-graphic></inline-formula>) is already decreasing below 1 due to a very low value of the transmission rate (<inline-formula><inline-graphic xlink:href="pone.0011655.e003.jpg" mimetype="image"></inline-graphic></inline-formula>) (<xref ref-type="fig" rid="pone-0011655-g001">Figure 1C and 1D</xref>). That is, in July the transmission is no longer effective even though there are plenty of susceptible persons. As such, the proportion of infectious persons that build up is not enough to generate many severe cases and the CFR is then maintained near 0.4% during the first wave in both scenarios (<xref ref-type="fig" rid="pone-0011655-g001">Figure 1A and 1B</xref>). During the second wave, on the other hand, <inline-formula><inline-graphic xlink:href="pone.0011655.e004.jpg" mimetype="image"></inline-graphic></inline-formula> is higher than 1 and the epidemic build up quickly. The second wave peaked in October and the mortality rate is then dependent on the value for simultaneous multiple contacts between a susceptible and infectious persons (<inline-formula><inline-graphic xlink:href="pone.0011655.e005.jpg" mimetype="image"></inline-graphic></inline-formula>).</p><fig id="pone-0011655-g001" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0011655.g001</object-id><label>Figure 1</label><caption><title>Incidence, mortality and case-fatality rate for influenza pandemic under different levels of multiple contacts between a susceptible person and infectious ones.</title><p>A and B gives the mortality rate and the case-fatality rate for scenarios 1 (<inline-formula><inline-graphic xlink:href="pone.0011655.e006.jpg" mimetype="image"></inline-graphic></inline-formula>) and 2 (<inline-formula><inline-graphic xlink:href="pone.0011655.e007.jpg" mimetype="image"></inline-graphic></inline-formula>). C and D gives the corresponding incidence per 100 000 persons in the population and the effective reproduction rate.</p></caption><graphic xlink:href="pone.0011655.g001"></graphic></fig><p>If the number of simultaneous contacts is decreased from <inline-formula><inline-graphic xlink:href="pone.0011655.e008.jpg" mimetype="image"></inline-graphic></inline-formula> to <inline-formula><inline-graphic xlink:href="pone.0011655.e009.jpg" mimetype="image"></inline-graphic></inline-formula> in the middle of the epidemic, there is a decrease in the mortality rate observed (<xref ref-type="fig" rid="pone-0011655-g002">Figure 2A</xref>). The total mortality rate among the population when <inline-formula><inline-graphic xlink:href="pone.0011655.e010.jpg" mimetype="image"></inline-graphic></inline-formula> was 4267 deaths per 100 000 persons whereas when <inline-formula><inline-graphic xlink:href="pone.0011655.e011.jpg" mimetype="image"></inline-graphic></inline-formula> decreased to 2 the total mortality rate decreased to 3773 deaths per 100 000 persons. Decrease in mortality is higher when the change in <inline-formula><inline-graphic xlink:href="pone.0011655.e012.jpg" mimetype="image"></inline-graphic></inline-formula> is implemented sooner in the epidemic and has no impact if it is implemented too late.</p><fig id="pone-0011655-g002" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0011655.g002</object-id><label>Figure 2</label><caption><title>Dynamics of influenza pandemic with varying <inline-formula><inline-graphic xlink:href="pone.0011655.e013.jpg" mimetype="image"></inline-graphic></inline-formula> and waning immunity.</title><p>A a change in the level of multiple contacts as soon as the number of deaths is above 500 from <inline-formula><inline-graphic xlink:href="pone.0011655.e014.jpg" mimetype="image"></inline-graphic></inline-formula> to <inline-formula><inline-graphic xlink:href="pone.0011655.e015.jpg" mimetype="image"></inline-graphic></inline-formula> and B a faster rate for waning immunity in a scenario where <inline-formula><inline-graphic xlink:href="pone.0011655.e016.jpg" mimetype="image"></inline-graphic></inline-formula>.</p></caption><graphic xlink:href="pone.0011655.g002"></graphic></fig><p>In the proposed model a third wave can occur as persons in the recovery compartment wane immunity. Nonetheless, the rate at which immunity is lost has to be high, in the order of 1 year in average (<xref ref-type="fig" rid="pone-0011655-g002">Figure 2B</xref>). If the rate is low (<xref ref-type="table" rid="pone-0011655-t001">table 1</xref>), there are only two waves (<xref ref-type="fig" rid="pone-0011655-g002">Figure 2</xref>), unless there is introduction of new susceptible persons in the population (<xref ref-type="fig" rid="pone-0011655-g003">Figure 3</xref>). If a group of persons became voluntarily isolated, for instance due to the perception of a high number of deaths, returning to the community some days later, several epidemic waves occurred. The number of epidemic waves will depend on the time of the epidemic people leave and return to the community. The lower the value of mortality that alert people leave the community, the higher the number of waves (<xref ref-type="fig" rid="pone-0011655-g003">Figure 3A and 3C</xref>). The CFR depends on the proportion of infectious persons in each wave and on <inline-formula><inline-graphic xlink:href="pone.0011655.e017.jpg" mimetype="image"></inline-graphic></inline-formula>. But, for the same transmission rate and population size, the more waves are build up the lower the chance a susceptible person has to make simultaneous contacts with infectious persons in each of the waves and lower the CFR. This is depicted in the simulations. The total number of deaths for <inline-formula><inline-graphic xlink:href="pone.0011655.e018.jpg" mimetype="image"></inline-graphic></inline-formula> without isolation, was 2984 deaths per 100 000 persons (<xref ref-type="fig" rid="pone-0011655-g001">Figure 1A</xref>), whereas with voluntary isolation there were 2947 deaths per 100 000 persons (<xref ref-type="fig" rid="pone-0011655-g003">Figure 3A</xref>). If people become isolated at different times during the epidemic, more waves were produced and less deaths occurred. In the scenario producing four waves there were 2884 deaths per 100 000 persons (<xref ref-type="fig" rid="pone-0011655-g003">Figure 3C</xref>).</p><fig id="pone-0011655-g003" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0011655.g003</object-id><label>Figure 3</label><caption><title>Dynamics of influenza pandemic with volunteer isolation.</title><p>A and B volunteer isolation started when the number of deaths was above 400 and persons returned to community when the number of deaths was bellow 100 and C and D volunteer isolation started when the number of deaths was above 200 and persons returned to community when the number of deaths was bellow 100. Arrows in B and D indicate the time at which persons leave and return to the susceptible compartment.</p></caption><graphic xlink:href="pone.0011655.g003"></graphic></fig><table-wrap id="pone-0011655-t001" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0011655.t001</object-id><label>Table 1</label><caption><title>Parameters used in the model.</title></caption><alternatives><graphic id="pone-0011655-t001-1" xlink:href="pone.0011655.t001"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1">Parameter</td><td align="left" rowspan="1" colspan="1">Value</td><td align="left" rowspan="1" colspan="1">Reference</td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e019.jpg" mimetype="image"></inline-graphic></inline-formula> Basic reproduction rate</td><td align="left" rowspan="1" colspan="1">2–5</td><td align="left" rowspan="1" colspan="1"><xref rid="pone.0011655-Andreasen1" ref-type="bibr">[50]</xref>, <xref rid="pone.0011655-Mills1" ref-type="bibr">[60]</xref></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e020.jpg" mimetype="image"></inline-graphic></inline-formula> Average period in latent compartment (days)</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1"><xref rid="pone.0011655-Carrat1" ref-type="bibr">[41]</xref></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e021.jpg" mimetype="image"></inline-graphic></inline-formula> Average period in infectious compartment (days)</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1"><xref rid="pone.0011655-Carrat1" ref-type="bibr">[41]</xref></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e022.jpg" mimetype="image"></inline-graphic></inline-formula> Rate of waning immunity (days)</td><td align="left" rowspan="1" colspan="1">9.7e-04 (mild), 4.8e-04 (severe)</td><td align="left" rowspan="1" colspan="1"><xref rid="pone.0011655-Davies1" ref-type="bibr">[51]</xref>–<xref rid="pone.0011655-Sonoguchi1" ref-type="bibr">[53]</xref></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e023.jpg" mimetype="image"></inline-graphic></inline-formula> Level of multiple contacts</td><td align="left" rowspan="1" colspan="1">2 and 8</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e024.jpg" mimetype="image"></inline-graphic></inline-formula> Proportion leaving the susceptible compartment</td><td align="left" rowspan="1" colspan="1">0.1</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e025.jpg" mimetype="image"></inline-graphic></inline-formula> Proportion returning to the susceptible compartment</td><td align="left" rowspan="1" colspan="1">0.1</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e026.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e027.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e028.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0011655.e029.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"></td></tr></tbody></table></alternatives></table-wrap></sec><sec id="s3"><title>Discussion</title><p>In this paper we proposed that severe cases resulting from an infection with influenza A virus of a naïve healthy individual is due to a higher infectious dose of the virus. Additionally, we proposed that the infectious dose is mediated by the number of simultaneous contacts established between a susceptible person and infectious ones. In this sense over-crowded places would have been ideal for a susceptible person to be exposed to very high infectious doses of influenza A virus. In 1918 the army camps fit the model by being characterised by a high number of contacts between people and by a high case-fatality rate, sometimes 5 to 8 times higher than the case-fatality rate among civilian communities <xref rid="pone.0011655-Kawana1" ref-type="bibr">[23]</xref>, <xref rid="pone.0011655-Barry1" ref-type="bibr">[24]</xref>. This difference in influenza-like illness mortality is sometimes associated to poor conditions in military base hospitals <xref rid="pone.0011655-Kawana1" ref-type="bibr">[23]</xref> or to a lower lung capacity of soldiers due to the inhalation of gases during the war <xref rid="pone.0011655-Oxford1" ref-type="bibr">[20]</xref>. However, of note, many of these reports were from training army camps <xref rid="pone.0011655-Barry1" ref-type="bibr">[24]</xref> where soldiers had health-care conditions similar to those offered to civilian communities. Differences in the CFR could also result from age related mortality since persons aged between 20–30 years old, similar to the soldiers age range, were the most severely affected during the 1918 influenza pandemic whereas among civilians the CFR might have be muted due to a wider age range. Nonetheless, even between civilian communities, factors such as crowding or continuous exposure, that can be viewed as favouring simultaneous contacts between a susceptible person and infectious ones, were associated to higher mortality rates. Rurality, for instance, was referred as a protective factor for the 1918 influenza pandemic mortality compared to urban areas <xref rid="pone.0011655-McSweeny1" ref-type="bibr">[25]</xref>–<xref rid="pone.0011655-Nishiura1" ref-type="bibr">[27]</xref>. In one of these papers the CFR was estimated and it was found that case-fatality rate was highest in larger towns followed by smaller towns and cities. Villages appeared to yield the lowest case fatality with an estimated 0.96 (0.82 1.09)% and the highest morbidity <xref rid="pone.0011655-Nishiura1" ref-type="bibr">[27]</xref>. This may be indicative that the chance to make simultaneous contacts between a susceptible person and infectious ones is higher in larger cities compared to villages. In villages, contacts are probably easily established between persons, enhancing transmission, but most probably involve, at each time, few infectious persons which diminishes <inline-formula><inline-graphic xlink:href="pone.0011655.e030.jpg" mimetype="image"></inline-graphic></inline-formula> and thus the CFR. We cannot, nonetheless, exclude other factors for the observed difference. Socio-demographic heterogeneity's such as a higher proportion of young people, poorer health and nutrition in urban areas may have also contribute to the difference in mortality between urban and rural areas <xref rid="pone.0011655-Nishiura1" ref-type="bibr">[27]</xref>. More examples that could be indicative of a higher mortality associated to a higher infectious dose include data from two parishes in Norway, where the number of rooms per apartment was associated to a higher mortality during the 1918 influenza pandemic <xref rid="pone.0011655-Mamelund1" ref-type="bibr">[28]</xref>, as well as an analysis of mortality data by family in Iceland, that lead the author <xref rid="pone.0011655-Gottfredsson1" ref-type="bibr">[29]</xref> to propose that the most important determinant of fatal outcome during the 1918 pandemic was associated to greater proximity or repeated exposure to infectious patients, possibly through greater infective dose of the virus, resulting in higher viral burden with “cytokine storm” and death. As in previous examples other factors such as economic level that could determine the nutrition status and access to health care services among persons living in smaller and crowding apartments cannot be excluded <xref rid="pone.0011655-Richard1" ref-type="bibr">[30]</xref>.</p><p>It is generally recognised that there is a minimum infectious dose able to produce infection in naturally occurring influenza in humans. The importance of this dose-dependence is the basis for some of the World Health Organisation recommendations for pandemic influenza interventions. Those interventions are aimed to reduce contacts with infectious individuals avoiding infection of other persons or delaying the spread of the virus and thus prevent disruption of health-care services <xref rid="pone.0011655-World2" ref-type="bibr">[31]</xref>. The effect of high infectious dose on influenza disease progression, on the other hand, have been shown in experimental animal models <xref rid="pone.0011655-Francis1" ref-type="bibr">[32]</xref>–<xref rid="pone.0011655-Ja1" ref-type="bibr">[39]</xref>. The dose-dependence is variable, depending on the site of inoculation <xref rid="pone.0011655-Yetter1" ref-type="bibr">[35]</xref>, the host background <xref rid="pone.0011655-Srivastava1" ref-type="bibr">[40]</xref>, the host age <xref rid="pone.0011655-Lu1" ref-type="bibr">[38]</xref> and the influenza virus type. Overall, a high infectious dose is associated to a higher viral load <xref rid="pone.0011655-Taylor1" ref-type="bibr">[33]</xref>, <xref rid="pone.0011655-Pinto1" ref-type="bibr">[34]</xref>, with a smaller period of time to maximum viral load <xref rid="pone.0011655-Taylor1" ref-type="bibr">[33]</xref>, <xref rid="pone.0011655-Pinto1" ref-type="bibr">[34]</xref> and with extensive clinical symptoms <xref rid="pone.0011655-Francis1" ref-type="bibr">[32]</xref>, <xref rid="pone.0011655-Pinto1" ref-type="bibr">[34]</xref>, <xref rid="pone.0011655-Ja1" ref-type="bibr">[39]</xref>. In volunteer challenge studies using humans, only the duration of virus shedding was found to be dose-dependent on the intranasal dose whereas the number of symptoms were more dependent on virus shedding <xref rid="pone.0011655-Carrat1" ref-type="bibr">[41]</xref>. Challenge studies in humans are difficult and results can be confounded by attenuation of the virus, the route of infection and previously acquired immunity <xref rid="pone.0011655-Carrat1" ref-type="bibr">[41]</xref>. Furthermore, volunteer challenge studies lead to mild or symptomless disease only and may not reflect naturally acquired influenza virus infection characterised by a spectrum of disease states, ranging from clinically symptomless illness through mild infection and to severe, even lethal, viral pneumonia. Ethical limitations in volunteer challenge studies are overcome by the use of mathematical models to reproduce the dynamics of the immune response against an infection with influenza A virus in humans. A robust result from simulations of these models point to an upper threshold on the infectious dose above which the proportion of damaged epithelial cells results in severe influenza disease <xref rid="pone.0011655-Hancioglu1" ref-type="bibr">[42]</xref>, <xref rid="pone.0011655-Chang1" ref-type="bibr">[43]</xref>. For a small infectious dose the disease progresses through an asymptomatic course and for intermediate values of infectious doses the outcome is variable <xref rid="pone.0011655-Hancioglu1" ref-type="bibr">[42]</xref> which could, in part, explain the lack of a clear dose-response in human studies.</p><p>In our model we assumed that the number of simultaneous contacts between a susceptible person and infectious ones is a proxy for influenza infectious dose. Influenza A virus spreads from person-to-person by droplet transmission <xref rid="pone.0011655-Brankston1" ref-type="bibr">[44]</xref>, aerosol transmission <xref rid="pone.0011655-Tellier1" ref-type="bibr">[45]</xref> or self-inoculation by contact with fomites or contaminated hands <xref rid="pone.0011655-Brankston1" ref-type="bibr">[44]</xref>, <xref rid="pone.0011655-Nicas1" ref-type="bibr">[46]</xref>. Both droplet transmission and transmission through contaminated hands needs close contact between susceptible and infectious persons and, although long-range transmission of aerosol particles is possible, the amount of virus sprayed in each sneeze is so small and is so rapidly diluted, as the aerosol disperses, that the risk of infection is probably significant only at the proximity of a susceptible person <xref rid="pone.0011655-Brankston1" ref-type="bibr">[44]</xref>, <xref rid="pone.0011655-Tellier1" ref-type="bibr">[45]</xref>.</p><p>In our model we also addressed waning immunity as a possible mechanism to explain a third wave. This mechanism has been previously used to fit a dynamical model to data on the 1918 influenza pandemic and the best fit estimated that the replenish of the susceptible pool due to waning immunity could occur in a time scale from weeks to months <xref rid="pone.0011655-Mathews1" ref-type="bibr">[47]</xref>. This rate is higher than the one we used in the model but in fact the only difference expected by increasing the rate of waning immunity is a higher morbidity during the third wave and thus a higher CFR, but still lower then the CFR during the second wave. An important aspect not covered by this modelling is the inclusion of asymptomatic cases <xref rid="pone.0011655-Mathews1" ref-type="bibr">[47]</xref>. If the infectious dose is very low we expect more asymptomatic infectious individuals <xref rid="pone.0011655-Hancioglu1" ref-type="bibr">[42]</xref> that in turn will decrease the attack rate, decreasing the number of infectious individuals and thus of severe cases.</p><p>Overall, nonetheless, the model reproduces the mechanism we want to show. In fact, according to the model structure case-fatality rate is a non-linear function of the number of infectious individuals, increasing at a higher rate when severe disease cases build-up. This structure differs from other mathematical models <xref rid="pone.0011655-Ferguson1" ref-type="bibr">[48]</xref>, <xref rid="pone.0011655-Halloran1" ref-type="bibr">[49]</xref> where case-fatality rate is a linear function of the number of infectious persons. This difference has important consequences when interpreting historical data on mortality and when considering strategies to mitigate influenza mortality. Case-fatality rate associated to the 1918 influenza pandemic has been estimated as being between 0.3% and 6% <xref rid="pone.0011655-Kawana1" ref-type="bibr">[23]</xref>, <xref rid="pone.0011655-Andreasen1" ref-type="bibr">[50]</xref>. Under this hypothesis, nonetheless, the CFR associated to severe disease has to be much higher than 6% to have in average an observed CFR of 6%. Also, as simulations showed, the number of severe cases, in each wave, decreased when the number of infections was spread along time, which resulted in a decrease of the overall CFR. Adoption of layered non-pharmaceutical interventions, like school closure and public gathering ban, earlier and in a sustained way, have been considered to reduce the attack rate of influenza among persons in the community <xref rid="pone.0011655-World2" ref-type="bibr">[31]</xref>. However, as simulated by mathematical models, the efficacy of these interventions are greatly dependent on the basic reproduction rate (<inline-formula><inline-graphic xlink:href="pone.0011655.e031.jpg" mimetype="image"></inline-graphic></inline-formula>) and on the starting time and duration of those interventions <xref rid="pone.0011655-Ferguson1" ref-type="bibr">[48]</xref>, <xref rid="pone.0011655-Halloran1" ref-type="bibr">[49]</xref>. In light of our hypothesis, nonetheless, non-pharmaceutical measures may be more important to reduce case-fatality rates than morbidity. Implementation of such interventions spreads the epidemic into a longer period, decreasing the number of infectious persons at each time in the epidemic, and consequently decreasing the number of severe influenza cases among healthy people and overall mortality.</p></sec><sec sec-type="materials|methods" id="s4"><title>Materials and Methods</title><sec id="s4a"><title>Transmission model</title><p>To illustrate this hypothesis we used a compartment model to study the spread of the influenza virus in a completely immunological naïve population, from invasion to one year later. (<xref ref-type="fig" rid="pone-0011655-g004">Figure 4</xref>). At the start of the simulations all individuals are susceptible to infection (S). After infection, susceptible individuals become exposed (E) for 2 days before becoming infectious (I). The infectious period (I) lasts for 5 days (<xref ref-type="table" rid="pone-0011655-t001">Table 1</xref>) and is followed by the recovery state (R) characterised by resistance to re-infection by an homotypic strain. There are two compartments for exposed, infectious and recovery states corresponding to mild and severe disease. In the model, both disease states are differentiated by the case-fatality rate and by the decay in the antibody titre. In human studies it was observed that after primary infection, antibody titre against an homotypic type decreased with time and three years after maximum antibody response antibody titre was not found in between 11 and 34% of previously infected individuals <xref rid="pone.0011655-Davies1" ref-type="bibr">[51]</xref>–<xref rid="pone.0011655-Sonoguchi1" ref-type="bibr">[53]</xref>. This observation is in agreement with earlier animal experiments were it was observed that the immune response of ferrets following influenza infection, with low or high infectious doses, was resistant to re-infection <xref rid="pone.0011655-Francis1" ref-type="bibr">[32]</xref>. Instead, the decay in antibody titre was accelerated for lower infectious doses <xref rid="pone.0011655-Francis1" ref-type="bibr">[32]</xref>. Accordingly, in the model, recovery from mild and severe infection was followed by an exponential rate of decay in antibody titre in a way that, respectively, at the end of one or three years, 70% of individuals are still resistant to infection (<xref ref-type="table" rid="pone-0011655-t001">table 1</xref>). The compartmental model is formalised by the following system of ordinary differential equations:<disp-formula><graphic xlink:href="pone.0011655.e032.jpg" mimetype="image" position="float"></graphic><label>(1)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e033.jpg" mimetype="image" position="float"></graphic><label>(2)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e034.jpg" mimetype="image" position="float"></graphic><label>(3)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e035.jpg" mimetype="image" position="float"></graphic><label>(4)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e036.jpg" mimetype="image" position="float"></graphic><label>(5)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e037.jpg" mimetype="image" position="float"></graphic><label>(6)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e038.jpg" mimetype="image" position="float"></graphic><label>(7)</label></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e039.jpg" mimetype="image" position="float"></graphic><label>(8)</label></disp-formula>where <inline-formula><inline-graphic xlink:href="pone.0011655.e040.jpg" mimetype="image"></inline-graphic></inline-formula> corresponds to the birth and death rate of hosts. The full parameter set is described in <xref ref-type="table" rid="pone-0011655-t001">table 1</xref>. The infection rate <inline-formula><inline-graphic xlink:href="pone.0011655.e041.jpg" mimetype="image"></inline-graphic></inline-formula> is given by <inline-formula><inline-graphic xlink:href="pone.0011655.e042.jpg" mimetype="image"></inline-graphic></inline-formula>. Voluntary isolation, that is the transfer of susceptible persons from S to H depend on the function <inline-formula><inline-graphic xlink:href="pone.0011655.e043.jpg" mimetype="image"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xlink:href="pone.0011655.e044.jpg" mimetype="image"></inline-graphic></inline-formula> given by;<disp-formula><graphic xlink:href="pone.0011655.e045.jpg" mimetype="image" position="float"></graphic></disp-formula><disp-formula><graphic xlink:href="pone.0011655.e046.jpg" mimetype="image" position="float"></graphic></disp-formula>where <inline-formula><inline-graphic xlink:href="pone.0011655.e047.jpg" mimetype="image"></inline-graphic></inline-formula> gives the total number of deaths at time <inline-formula><inline-graphic xlink:href="pone.0011655.e048.jpg" mimetype="image"></inline-graphic></inline-formula>.</p><fig id="pone-0011655-g004" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0011655.g004</object-id><label>Figure 4</label><caption><title>Compartment model for influenza.</title><p>Each compartment correspond to a class of individuals in the population and arrows indicates transfer of individuals (<xref ref-type="table" rid="pone-0011655-t001">table 1</xref>). In summary S stands for susceptible, E for exposed, I for infectious and R for recovery. The subscript 1 and 2 stands for mild and severe disease. The transfer of individuals from S to H is always 0 except for two scenarios where we assumed that persons after perceiving a higher number of deaths leave the community and become voluntarily isolated. Details on the model are given in the <xref ref-type="sec" rid="s4">Methods</xref>.</p></caption><graphic xlink:href="pone.0011655.g004"></graphic></fig><p>We used BerKeley Madonna v8.3.12 with autostepsise method to find the numerical results of the model. Initial conditions for the system are given by <inline-formula><inline-graphic xlink:href="pone.0011655.e049.jpg" mimetype="image"></inline-graphic></inline-formula>, <inline-formula><inline-graphic xlink:href="pone.0011655.e050.jpg" mimetype="image"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xlink:href="pone.0011655.e051.jpg" mimetype="image"></inline-graphic></inline-formula>. The total population size is <inline-formula><inline-graphic xlink:href="pone.0011655.e052.jpg" mimetype="image"></inline-graphic></inline-formula>.</p></sec><sec id="s4b"><title>Simultaneous contacts</title><p>We assumed there is a minimum dose of virus necessary to cause severe infection, and bellow that dose the disease is mild. Severe disease is characterised by a case-fatality rate <inline-formula><inline-graphic xlink:href="pone.0011655.e053.jpg" mimetype="image"></inline-graphic></inline-formula> whereas mild disease is characterised by a case-fatality rate of <inline-formula><inline-graphic xlink:href="pone.0011655.e054.jpg" mimetype="image"></inline-graphic></inline-formula>.</p><p>To model the aggregation of infectious individuals around susceptible persons we used a saturating function of the Holling type II function <xref rid="pone.0011655-Renshaw1" ref-type="bibr">[54]</xref> that is used in population dynamics to model the ability of preys to escape the predator. The Holling type II function is given by<disp-formula><graphic xlink:href="pone.0011655.e055.jpg" mimetype="image" position="float"></graphic></disp-formula>The function <inline-formula><inline-graphic xlink:href="pone.0011655.e056.jpg" mimetype="image"></inline-graphic></inline-formula> becomes saturated for sufficient large proportion of infectious individuals which was interpreted by a limit in the number of social contacts a susceptible person can established, simultaneously, with infectious persons. This social limit is given by <inline-formula><inline-graphic xlink:href="pone.0011655.e057.jpg" mimetype="image"></inline-graphic></inline-formula>. The reason to use this function is as follows. The standard infection rate, <inline-formula><inline-graphic xlink:href="pone.0011655.e058.jpg" mimetype="image"></inline-graphic></inline-formula>, used in epidemiological models, is based on the law of mass action and determines that pairs of individuals interact through chance encounters. This law is only valid for low “concentrations” (e.g., in chemistry, dilute solutions), where simultaneous interactions of three or more individuals have negligible probability. In the context of this work, the relevant interaction of multiple individuals is the simultaneous interaction of a susceptible individual with <inline-formula><inline-graphic xlink:href="pone.0011655.e059.jpg" mimetype="image"></inline-graphic></inline-formula> infectious individuals. This is a subset of the pair-wise interactions (i.e., some of the pair-wise interactions are also <inline-formula><inline-graphic xlink:href="pone.0011655.e060.jpg" mimetype="image"></inline-graphic></inline-formula> wise interactions). For values of <inline-formula><inline-graphic xlink:href="pone.0011655.e061.jpg" mimetype="image"></inline-graphic></inline-formula> near zero, the social limit is so constrained that there are no interactions of more that two individuals and, even when the number of infectious individuals is very large, all interactions are just pair-wise and there are no severe cases of influenza. At the opposite extreme, when <inline-formula><inline-graphic xlink:href="pone.0011655.e062.jpg" mimetype="image"></inline-graphic></inline-formula> is very large, there is no limit on these interactions, and so, when almost all individuals in the population are infectious, almost all susceptible individuals develop severe influenza.</p></sec><sec id="s4c"><title>Seasonality</title><p>Influenza virus activity displays pronounced seasonal cycles in temperate areas with a peak in incidence during winter months. Such seasonal behaviour has been associated with temperature and humidity <xref rid="pone.0011655-Weber1" ref-type="bibr">[55]</xref>–<xref rid="pone.0011655-Lipsitch1" ref-type="bibr">[57]</xref>, to changes in mixing patterns like school terms <xref rid="pone.0011655-Lipsitch1" ref-type="bibr">[57]</xref>, <xref rid="pone.0011655-Vynnycky1" ref-type="bibr">[58]</xref>, increased viral production under winter conditions <xref rid="pone.0011655-Dushoff1" ref-type="bibr">[59]</xref> or simply driven by resonance caused by under-detected and small seasonal changes in transmission <xref rid="pone.0011655-Dushoff1" ref-type="bibr">[59]</xref>. We introduced seasonality into the model by assuming that virus transmissibility varies periodically with an yearly cycle. To this end, we modelled the contact rate with a sinusoidal function<disp-formula><graphic xlink:href="pone.0011655.e063.jpg" mimetype="image" position="float"></graphic></disp-formula>where, the two parameters <inline-formula><inline-graphic xlink:href="pone.0011655.e064.jpg" mimetype="image"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xlink:href="pone.0011655.e065.jpg" mimetype="image"></inline-graphic></inline-formula> represent the baseline rate of transmission and the amplitude of seasonality, respectively. The function <inline-formula><inline-graphic xlink:href="pone.0011655.e066.jpg" mimetype="image"></inline-graphic></inline-formula> has period of 365 days. Simulations start at 1st May (<inline-formula><inline-graphic xlink:href="pone.0011655.e067.jpg" mimetype="image"></inline-graphic></inline-formula>) and transmission has a maximum value 260 days after, in 1st January and a minimum value, 75 days after, in 1st July. The values for the <inline-formula><inline-graphic xlink:href="pone.0011655.e068.jpg" mimetype="image"></inline-graphic></inline-formula> parameters were adjusted such that the seasonally-varying basic reproductive number over an annual cycle summed to <inline-formula><inline-graphic xlink:href="pone.0011655.e069.jpg" mimetype="image"></inline-graphic></inline-formula> with an amplitude in the range between 1 and 5 <xref rid="pone.0011655-Andreasen1" ref-type="bibr">[50]</xref>, <xref rid="pone.0011655-Mills1" ref-type="bibr">[60]</xref>, <xref rid="pone.0011655-White1" ref-type="bibr">[61]</xref>. The transmission rate was then scaled according to<disp-formula><graphic xlink:href="pone.0011655.e070.jpg" mimetype="image" position="float"></graphic></disp-formula>for this model structure the effective reproduction number <inline-formula><inline-graphic xlink:href="pone.0011655.e071.jpg" mimetype="image"></inline-graphic></inline-formula>, that is the number of cases an infectious individual can generate in a non-susceptible population is given by the <inline-formula><inline-graphic xlink:href="pone.0011655.e072.jpg" mimetype="image"></inline-graphic></inline-formula>.</p></sec><sec id="s4d"><title>Methodological overview</title><p>We modelled two scenarios (<xref ref-type="fig" rid="pone-0011655-g002">Figure 2</xref>) corresponding to two different values of the parameter <inline-formula><inline-graphic xlink:href="pone.0011655.e073.jpg" mimetype="image"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xlink:href="pone.0011655.e074.jpg" mimetype="image"></inline-graphic></inline-formula>, that is the number of simultaneous contacts between a susceptible and infectious persons. A third scenario was simulated by decreasing the value of <inline-formula><inline-graphic xlink:href="pone.0011655.e075.jpg" mimetype="image"></inline-graphic></inline-formula> as soon as the total number of deaths increases above 200 (<xref ref-type="fig" rid="pone-0011655-g003">Figure 3A</xref>) and a fourth and fifth scenario by allowing voluntary isolation and return to community at two different times in the epidemic (<xref ref-type="fig" rid="pone-0011655-g004">Figure 4</xref>). In the fourth scenario persons left the community when the total number of deaths was higher then 200 (<inline-formula><inline-graphic xlink:href="pone.0011655.e076.jpg" mimetype="image"></inline-graphic></inline-formula>) and return when the number of deaths was bellow 100 (<inline-formula><inline-graphic xlink:href="pone.0011655.e077.jpg" mimetype="image"></inline-graphic></inline-formula>), and in the fifth scenario persons left the community when the total number of deaths was above 400 (<inline-formula><inline-graphic xlink:href="pone.0011655.e078.jpg" mimetype="image"></inline-graphic></inline-formula>) and return when the total number of deaths was bellow 100. The last scenario was simulated by allowing a faster decay in antibody titre (<xref ref-type="fig" rid="pone-0011655-g003">Figure 3B</xref>). For severe disease antibody decay was set to <inline-formula><inline-graphic xlink:href="pone.0011655.e079.jpg" mimetype="image"></inline-graphic></inline-formula> years and for mild disease to <inline-formula><inline-graphic xlink:href="pone.0011655.e080.jpg" mimetype="image"></inline-graphic></inline-formula> years. Incidence was estimated as the number of infectious persons per 100 000 persons, mortality rate was estimated by the number of deaths by 100 000 persons and case-fatality rate (CFR) was estimated as the proportion of deaths among infectious persons.</p></sec></sec></body><back><ack><p>We thank Paula Rodrigues, Nuno Sousa, Joana Palha, Nadine Santos and the anonymous reviewers for advice on the manuscript.</p></ack><fn-group><fn fn-type="COI-statement"><p><bold>Competing Interests: </bold>The authors have declared that no competing interests exist.</p></fn><fn fn-type="financial-disclosure"><p><bold>Funding: </bold>TD acknowledges the support of the Faculdade de Ciências e Tecnologia through grant PPCDT/AMB/55701/2004. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.</p></fn></fn-group><ref-list><title>References</title><ref id="pone.0011655-Potter1"><label>1</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Potter</surname><given-names>CW</given-names></name></person-group><year>2001</year><article-title>A history of influenza.</article-title><source>J Appl Microbiol</source><volume>91</volume><fpage>572</fpage><lpage>579</lpage><pub-id pub-id-type="pmid">11576290</pub-id></element-citation></ref><ref id="pone.0011655-Kilbourne1"><label>2</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kilbourne</surname><given-names>ED</given-names></name></person-group><year>2006</year><article-title>Influenza pandemics of the 20th century.</article-title><source>Emerg Infect Dis</source><volume>12</volume><fpage>8</fpage><lpage>14</lpage></element-citation></ref><ref id="pone.0011655-Ansart1"><label>3</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ansart</surname><given-names>S</given-names></name><name><surname>Pelat</surname><given-names>C</given-names></name><name><surname>Boelle</surname><given-names>PY</given-names></name><name><surname>Carrat</surname><given-names>F</given-names></name><name><surname>Flahault</surname><given-names>A</given-names></name><etal></etal></person-group><year>2009</year><article-title>Mortality burden of the 1918–1919 influenza pandemic in Europe.</article-title><source>Influenza Other Respi Viruses</source><volume>3</volume><fpage>99</fpage><lpage>106</lpage></element-citation></ref><ref id="pone.0011655-Miller1"><label>4</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Miller</surname><given-names>MA</given-names></name><name><surname>Viboud</surname><given-names>C</given-names></name><name><surname>Balinska</surname><given-names>M</given-names></name><name><surname>Simonsen</surname><given-names>L</given-names></name></person-group><year>2009</year><article-title>The Signature Features of Influenza Pandemics - implications for policy.</article-title><source>N Engl J Med</source><volume>360</volume><fpage>2595</fpage><lpage>2598</lpage><pub-id pub-id-type="pmid">19423872</pub-id></element-citation></ref><ref id="pone.0011655-Taubenberger1"><label>5</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Taubenberger</surname><given-names>JK</given-names></name><name><surname>Morens</surname><given-names>D</given-names></name></person-group><year>2006</year><article-title>1918 Influenza: the mother of all pandemics.</article-title><source>Emerg Infect Dis</source><volume>12</volume><fpage>15</fpage><lpage>22</lpage><pub-id pub-id-type="pmid">16494711</pub-id></element-citation></ref><ref id="pone.0011655-Murray1"><label>6</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Murray</surname><given-names>CJL</given-names></name><name><surname>Lopez</surname><given-names>AD</given-names></name><name><surname>Chin</surname><given-names>B</given-names></name><name><surname>Feehan</surname><given-names>D</given-names></name><name><surname>Hill</surname><given-names>KH</given-names></name></person-group><year>2006</year><article-title>Estimation of potential global pandemic influenza mortality on the basis of vital registry data from the 1918 20 pandemic : a quantitative analysis.</article-title><source>Lancet</source><volume>368</volume><fpage>2211</fpage><lpage>2218</lpage><pub-id pub-id-type="pmid">17189032</pub-id></element-citation></ref><ref id="pone.0011655-Payne1"><label>7</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Payne</surname><given-names>AMM</given-names></name></person-group><year>1958</year><article-title>Some aspects of the epidemiology of the 1957 Influenza pandemic.</article-title><source>Proc R Soc Med</source><volume>51</volume><fpage>29</fpage></element-citation></ref><ref id="pone.0011655-Viboud1"><label>8</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Viboud</surname><given-names>C</given-names></name><name><surname>Grais</surname><given-names>RF</given-names></name><name><surname>Lafont</surname><given-names>BAP</given-names></name><name><surname>Miller</surname><given-names>MA</given-names></name><name><surname>Simonsen</surname><given-names>L</given-names></name></person-group><year>2005</year><article-title>Multinational Impact of the 1968 Hong Kong Influenza Pandemic : Evidence for a Smoldering Pandemic.</article-title><source>J Infect Dis</source><volume>192</volume><fpage>233</fpage><lpage>248</lpage><pub-id pub-id-type="pmid">15962218</pub-id></element-citation></ref><ref id="pone.0011655-World1"><label>9</label><element-citation publication-type="other"><collab>World Health Organization</collab><year>2005</year><article-title>Avian influenza: assessing the pandemic threat.</article-title><comment>Technical Report CDS 2005.29, World Health Organization</comment></element-citation></ref><ref id="pone.0011655-Kobasa1"><label>10</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kobasa</surname><given-names>D</given-names></name><name><surname>Takada</surname><given-names>A</given-names></name><name><surname>Shinya</surname><given-names>K</given-names></name><name><surname>Hatta</surname><given-names>M</given-names></name><name><surname>Halfmann</surname><given-names>P</given-names></name><etal></etal></person-group><year>2004</year><article-title>Enhanced virulence of influenza A viruses with the haemagglutinin of the 1918 pandemic virus.</article-title><source>Nature</source><volume>431</volume><fpage>703</fpage><lpage>707</lpage><pub-id pub-id-type="pmid">15470432</pub-id></element-citation></ref><ref id="pone.0011655-Tumpey1"><label>11</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tumpey</surname><given-names>TM</given-names></name><name><surname>Garcia-Sastre</surname><given-names>A</given-names></name><name><surname>Taubenberger</surname><given-names>JK</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name><name><surname>Swayne</surname><given-names>DE</given-names></name><etal></etal></person-group><year>2005</year><article-title>Pathogenicity of influenza viruses with genes from the 1918 pandemic virus: functional roles of alveolar macrophages and neutrophils in limiting virus replication and mortality in mice.</article-title><source>J Virol</source><volume>79</volume><fpage>14933</fpage><lpage>14944</lpage><pub-id pub-id-type="pmid">16282492</pub-id></element-citation></ref><ref id="pone.0011655-Kobasa2"><label>12</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kobasa</surname><given-names>D</given-names></name><name><surname>Jones</surname><given-names>SM</given-names></name><name><surname>Shinya</surname><given-names>K</given-names></name><name><surname>Kash</surname><given-names>JC</given-names></name><name><surname>Copps</surname><given-names>J</given-names></name><etal></etal></person-group><year>2007</year><article-title>Aberrant innate immune response in lethal infection of macaques with the 1918 influenza virus.</article-title><source>Nature</source><volume>445</volume><fpage>319</fpage><lpage>323</lpage><pub-id pub-id-type="pmid">17230189</pub-id></element-citation></ref><ref id="pone.0011655-Morens1"><label>13</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Morens</surname><given-names>DM</given-names></name><name><surname>Taubenberger</surname><given-names>JK</given-names></name><name><surname>Fauci</surname><given-names>AS</given-names></name></person-group><year>2008</year><article-title>Predominant role of bacterial pneumonia as a cause of death in pandemic influenza: implications for pandemic influenza preparedness.</article-title><source>J Infect Dis</source><volume>198</volume><fpage>962</fpage><lpage>970</lpage><pub-id pub-id-type="pmid">18710327</pub-id></element-citation></ref><ref id="pone.0011655-Klugman1"><label>14</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Klugman</surname><given-names>KP</given-names></name><name><surname>Astley</surname><given-names>M</given-names></name><name><surname>Lipsitch</surname><given-names>M</given-names></name></person-group><year>2009</year><article-title>Time from Illness Onset to Death , 1918 Infl uenza and Pneumococcal Pneumonia Unusual Manifestation of Toscana Virus Infection , Spain.</article-title><source>Emerg Infect Dis</source><volume>15</volume><fpage>346</fpage><lpage>347</lpage><pub-id pub-id-type="pmid">19193293</pub-id></element-citation></ref><ref id="pone.0011655-Gibbs1"><label>15</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gibbs</surname><given-names>MJ</given-names></name><name><surname>Armstrong</surname><given-names>JS</given-names></name><name><surname>Gibbs</surname><given-names>AJ</given-names></name></person-group><year>2001</year><article-title>Recombination in the Hemagglutinin Gene of the 1918 “Spanish Flu”.</article-title><source>Science</source><volume>293</volume><fpage>1842</fpage><lpage>1845</lpage><pub-id pub-id-type="pmid">11546876</pub-id></element-citation></ref><ref id="pone.0011655-Enserink1"><label>16</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Enserink</surname><given-names>M</given-names></name></person-group><year>2007</year><article-title>From two mutations, an important clus about the Spanish flu.</article-title><source>Science</source><volume>315</volume><fpage>582</fpage><pub-id pub-id-type="pmid">17272689</pub-id></element-citation></ref><ref id="pone.0011655-Tumpey2"><label>17</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tumpey</surname><given-names>TM</given-names></name><name><surname>Maines</surname><given-names>TR</given-names></name><name><surname>Hoeven</surname><given-names>NV</given-names></name><name><surname>Glaser</surname><given-names>L</given-names></name><name><surname>Solórzano</surname><given-names>A</given-names></name><etal></etal></person-group><year>2007</year><article-title>A Two-Amino Acid Change in the Hemagglutinin of the 1918 Influenza Virus Abolishes Transmission.</article-title><source>Science</source><volume>315</volume><fpage>655</fpage><lpage>659</lpage><pub-id pub-id-type="pmid">17272724</pub-id></element-citation></ref><ref id="pone.0011655-Taubenberger2"><label>18</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Taubenberger</surname><given-names>JK</given-names></name><name><surname>Reid</surname><given-names>AH</given-names></name><name><surname>Janczewski</surname><given-names>TA</given-names></name><name><surname>Fanning</surname><given-names>TG</given-names></name></person-group><year>2001</year><article-title>Integrating historical, clinical and molecular genetic data in order to explain the origin and virulence of the 1918 Spanish influenza virus.</article-title><source>Philos Trans R Soc Lond B Biol Sci</source><volume>356</volume><fpage>1829</fpage><lpage>1839</lpage><pub-id pub-id-type="pmid">11779381</pub-id></element-citation></ref><ref id="pone.0011655-Reid1"><label>19</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Reid</surname><given-names>AH</given-names></name><name><surname>Janczewski</surname><given-names>TA</given-names></name><name><surname>Lorens</surname><given-names>RM</given-names></name><name><surname>J</surname><given-names>EA</given-names></name><name><surname>Daniels</surname><given-names>RS</given-names></name><etal></etal></person-group><year>2003</year><article-title>1918 Influenza pandemic caused by highly conserved viruses with two receptor-binding variants.</article-title><source>Emerg Infect Dis</source><volume>9</volume><fpage>1249</fpage><lpage>1253</lpage><pub-id pub-id-type="pmid">14609459</pub-id></element-citation></ref><ref id="pone.0011655-Oxford1"><label>20</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Oxford</surname><given-names>JS</given-names></name><name><surname>Lambkin</surname><given-names>R</given-names></name><name><surname>Sefton</surname><given-names>A</given-names></name><name><surname>Daniels</surname><given-names>R</given-names></name><name><surname>Elliot</surname><given-names>A</given-names></name><etal></etal></person-group><year>2005</year><article-title>A hypothesis : the conjunction of soldiers, gas, pigs, ducks, geese and horses in Northern France during the Great War provided the conditions for the emergence of the Spanish influenza pandemic of 1918 1919.</article-title><source>Vaccine</source><volume>23</volume><fpage>940</fpage><lpage>945</lpage><pub-id pub-id-type="pmid">15603896</pub-id></element-citation></ref><ref id="pone.0011655-Oxford2"><label>21</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Oxford</surname><given-names>JS</given-names></name><name><surname>Sefton</surname><given-names>A</given-names></name><name><surname>Jackson</surname><given-names>R</given-names></name><name><surname>Innes</surname><given-names>W</given-names></name><name><surname>Daniels</surname><given-names>RS</given-names></name><etal></etal></person-group><year>2002</year><article-title>World War I may have allowed the emergence of Spanish influenza.</article-title><source>Lancet</source><volume>2</volume><fpage>111</fpage><lpage>114</lpage><pub-id pub-id-type="pmid">11901642</pub-id></element-citation></ref><ref id="pone.0011655-Markel1"><label>22</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Markel</surname><given-names>H</given-names></name><name><surname>Lipman</surname><given-names>HB</given-names></name><name><surname>Navarro</surname><given-names>JA</given-names></name><name><surname>Sloan</surname><given-names>A</given-names></name><name><surname>Michalsen</surname><given-names>JR</given-names></name><etal></etal></person-group><year>2007</year><article-title>Nonpharmaceutical Interventions Implemented by US Cities During the 1918–1919 Influenza Pandemic.</article-title><source>JAMA</source><volume>298</volume><fpage>644</fpage><lpage>654</lpage><pub-id pub-id-type="pmid">17684187</pub-id></element-citation></ref><ref id="pone.0011655-Kawana1"><label>23</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kawana</surname><given-names>A</given-names></name><name><surname>Naka</surname><given-names>G</given-names></name><name><surname>Fujikura</surname><given-names>Y</given-names></name><name><surname>Kato</surname><given-names>Y</given-names></name><name><surname>Mizuno</surname><given-names>Y</given-names></name><etal></etal></person-group><year>2007</year><article-title>Spanish Influenza in Japanese Armed Forces, 1918–1920.</article-title><source>Emerg Infect Dis</source><volume>13</volume><fpage>590</fpage><lpage>593</lpage><pub-id pub-id-type="pmid">17553274</pub-id></element-citation></ref><ref id="pone.0011655-Barry1"><label>24</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Barry</surname><given-names>JM</given-names></name><name><surname>Viboud</surname><given-names>C</given-names></name><name><surname>Simonsen</surname><given-names>L</given-names></name></person-group><year>2008</year><article-title>Cross-protection between successive waves of the 1918–1919 influenza pandemic: epidemiological evidence from US Army Camps and from Britain.</article-title><source>J Infect Dis</source><volume>198</volume><fpage>1427</fpage><lpage>1434</lpage><pub-id pub-id-type="pmid">18808337</pub-id></element-citation></ref><ref id="pone.0011655-McSweeny1"><label>25</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McSweeny</surname><given-names>K</given-names></name><name><surname>Colman</surname><given-names>A</given-names></name><name><surname>Fancourt</surname><given-names>N</given-names></name><name><surname>Parnell</surname><given-names>M</given-names></name><name><surname>Stantiall</surname><given-names>S</given-names></name><etal></etal></person-group><year>2007</year><article-title>Was rurality protective in the 1918 influenza pandemic in New Zealand?</article-title><source>N Z Med J</source><volume>120</volume><fpage>U2579</fpage><pub-id pub-id-type="pmid">17589547</pub-id></element-citation></ref><ref id="pone.0011655-Chowell1"><label>26</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chowell</surname><given-names>G</given-names></name><name><surname>Bettencourt</surname><given-names>LMA</given-names></name><name><surname>Johnson</surname><given-names>N</given-names></name><name><surname>Alonso</surname><given-names>WJ</given-names></name><name><surname>Viboud</surname><given-names>C</given-names></name></person-group><year>2008</year><article-title>The 1918–1919 influenza pandemic in England and Wales: spatial patterns in transmissibility and mortality impact.</article-title><source>Proc Biol Sci</source><volume>275</volume><fpage>501</fpage><lpage>9</lpage><pub-id pub-id-type="pmid">18156123</pub-id></element-citation></ref><ref id="pone.0011655-Nishiura1"><label>27</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H</given-names></name><name><surname>Chowell</surname><given-names>G</given-names></name></person-group><year>2008</year><article-title>Rurality and pandemic influenza: geographic heterogeneity in the risks of infection and death in Kanagawa, Japan (1918–1919).</article-title><source>N Z Med J</source><volume>121</volume><fpage>18</fpage><lpage>27</lpage></element-citation></ref><ref id="pone.0011655-Mamelund1"><label>28</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mamelund</surname><given-names>SE</given-names></name></person-group><year>2006</year><article-title>Social factors, mortality and the Spanish influenza in Kristiania 1918–19.</article-title><source>Soc Sci Med</source><volume>62</volume><fpage>923</fpage><lpage>940</lpage><pub-id pub-id-type="pmid">16084634</pub-id></element-citation></ref><ref id="pone.0011655-Gottfredsson1"><label>29</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gottfredsson</surname><given-names>M</given-names></name><name><surname>Halldorsson</surname><given-names>BV</given-names></name><name><surname>Jonsson</surname><given-names>S</given-names></name><name><surname>Kristjansson</surname><given-names>M</given-names></name><name><surname>Kristjansson</surname><given-names>K</given-names></name><etal></etal></person-group><year>2008</year><article-title>Lessons from the past : Familial aggregation analysis of fatal pandemic influenza ( Spanish flu ) in Iceland in 1918.</article-title><source>PNAS</source><volume>105</volume><fpage>1303</fpage><lpage>1308</lpage><pub-id pub-id-type="pmid">18216264</pub-id></element-citation></ref><ref id="pone.0011655-Richard1"><label>30</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Richard</surname><given-names>SA</given-names></name><name><surname>Sugaya</surname><given-names>N</given-names></name><name><surname>Simonsen</surname><given-names>L</given-names></name><name><surname>Miller</surname><given-names>MA</given-names></name><name><surname>Viboud</surname><given-names>C</given-names></name></person-group><year>2009</year><article-title>A comparative study of the 1918 1920 influenza pandemic in Japan , USA and UK : mortality impact and implications for pandemic planning.</article-title><source>Epidemiol Infect</source><volume>137</volume><fpage>1062</fpage><lpage>1072</lpage><pub-id pub-id-type="pmid">19215637</pub-id></element-citation></ref><ref id="pone.0011655-World2"><label>31</label><element-citation publication-type="journal"><collab>World Health Organization Writting Group</collab><year>2006</year><article-title>Nonpharmaceutical Interventions for Pandemic Influenza , National and Community Measures.</article-title><source>Emerg Infect Dis</source><volume>12</volume><fpage>88</fpage><lpage>94</lpage><pub-id pub-id-type="pmid">16494723</pub-id></element-citation></ref><ref id="pone.0011655-Francis1"><label>32</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Francis</surname><given-names>BYT</given-names></name></person-group><year>1938</year><article-title>Quantitative relationships between the immunizing dose of epidemic influenza and resultant immunity.</article-title><source>J Exp Med</source><volume>69</volume><fpage>283</fpage><lpage>300</lpage></element-citation></ref><ref id="pone.0011655-Taylor1"><label>33</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Taylor</surname><given-names>RM</given-names></name></person-group><year>1941</year><article-title>Experimental infection with influenza A virus in mice: the increase in intrapulmonary virus after inoculation and the influenza of various factors thereon.</article-title><source>J Exp Med</source><volume>73</volume><fpage>43</fpage><lpage>55</lpage><pub-id pub-id-type="pmid">19871064</pub-id></element-citation></ref><ref id="pone.0011655-Pinto1"><label>34</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pinto</surname><given-names>CA</given-names></name><name><surname>Haff</surname><given-names>RF</given-names></name><name><surname>Stewart</surname><given-names>RC</given-names></name></person-group><year>1969</year><article-title>Pathogenesis of and Recovery from Respiratory Syncytial and Influenza Infections in Ferrets.</article-title><source>Archiv für die gesamte Virusforschung</source><volume>26</volume><fpage>225</fpage><lpage>237</lpage></element-citation></ref><ref id="pone.0011655-Yetter1"><label>35</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yetter</surname><given-names>Ra</given-names></name><name><surname>Lehrer</surname><given-names>S</given-names></name><name><surname>Ramphal</surname><given-names>R</given-names></name><name><surname>Small</surname><given-names>PA</given-names></name></person-group><year>1980</year><article-title>Outcome of influenza infection: effect of site of initial infection and heterotypic immunity.</article-title><source>Infect Immun</source><volume>29</volume><fpage>654</fpage><lpage>62</lpage><pub-id pub-id-type="pmid">7216433</pub-id></element-citation></ref><ref id="pone.0011655-Oh1"><label>36</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Oh</surname><given-names>S</given-names></name><name><surname>McCaffery</surname><given-names>JM</given-names></name><name><surname>Eichelberger</surname><given-names>MC</given-names></name></person-group><year>2000</year><article-title>Dose-Dependent changes in influenza virus-infected denditric cells result in increased allogenic T-cell proliferation at low, but not at high, dose of virus.</article-title><source>J Virol</source><volume>74</volume><fpage>5460</fpage><lpage>5469</lpage><pub-id pub-id-type="pmid">10823850</pub-id></element-citation></ref><ref id="pone.0011655-Wattrang1"><label>37</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wattrang</surname><given-names>E</given-names></name><name><surname>Jessett</surname><given-names>DM</given-names></name><name><surname>Yates</surname><given-names>P</given-names></name><name><surname>Fuxler</surname><given-names>L</given-names></name><name><surname>Hannant</surname><given-names>D</given-names></name></person-group><year>2003</year><article-title>Experimental infection of ponies with equine influenza A2 (H3N8) virus strains of different pathogenicity elicits varying interferon and interleukin-6 responses.</article-title><source>Viral Immunol</source><volume>16</volume><fpage>57</fpage><lpage>67</lpage><pub-id pub-id-type="pmid">12725689</pub-id></element-citation></ref><ref id="pone.0011655-Lu1"><label>38</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lu</surname><given-names>H</given-names></name><name><surname>Castro</surname><given-names>AE</given-names></name></person-group><year>2004</year><article-title>Evaluation of the infectivity, length of infection, and immune response of a low-pathogenicity H7N2 Avian Influenza virus in specific-pathogen-free chickens.</article-title><source>Avian Dis</source><volume>48</volume><fpage>263</fpage><lpage>270</lpage><pub-id pub-id-type="pmid">15283413</pub-id></element-citation></ref><ref id="pone.0011655-Ja1"><label>39</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ja</surname><given-names>M</given-names></name><name><surname>D</surname><given-names>H</given-names></name><name><surname>Dm</surname><given-names>J</given-names></name></person-group><year>1990</year><article-title>Experimental infection of ponies with equine influenza ( H3N8 ) viruses by intranasal inoculation or exposure to aerosols.</article-title><source>Equine Vet J</source><volume>22</volume><fpage>93</fpage><lpage>98</lpage><pub-id pub-id-type="pmid">2156688</pub-id></element-citation></ref><ref id="pone.0011655-Srivastava1"><label>40</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Srivastava</surname><given-names>B</given-names></name><name><surname>Blazejewska</surname><given-names>P</given-names></name><name><surname>Hebmann</surname><given-names>M</given-names></name><name><surname>Bruder</surname><given-names>D</given-names></name><name><surname>Geffers</surname><given-names>R</given-names></name><etal></etal></person-group><year>2009</year><article-title>Host genetic background strongly influences the response to influenza A virus infections.</article-title><source>PLoS One</source><volume>4</volume><fpage>e485</fpage></element-citation></ref><ref id="pone.0011655-Carrat1"><label>41</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Carrat</surname><given-names>F</given-names></name><name><surname>Vergu</surname><given-names>E</given-names></name><name><surname>Ferguson</surname><given-names>NM</given-names></name><name><surname>Lemaitre</surname><given-names>M</given-names></name><name><surname>Cauchemez</surname><given-names>S</given-names></name><etal></etal></person-group><year>2008</year><article-title>Time lines of infection and disease in human influenza: a review of volunteer challenge studies.</article-title><source>Am J Epidemiol</source><volume>167</volume><fpage>775</fpage><lpage>85</lpage><pub-id pub-id-type="pmid">18230677</pub-id></element-citation></ref><ref id="pone.0011655-Hancioglu1"><label>42</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hancioglu</surname><given-names>B</given-names></name><name><surname>Swigon</surname><given-names>D</given-names></name><name><surname>Clermont</surname><given-names>G</given-names></name></person-group><year>2007</year><article-title>A dynamical model of human immune response to influenza A virus infection.</article-title><source>J Theor Biol</source><volume>246</volume><fpage>70</fpage><lpage>86</lpage><pub-id pub-id-type="pmid">17266989</pub-id></element-citation></ref><ref id="pone.0011655-Chang1"><label>43</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chang</surname><given-names>DB</given-names></name><name><surname>Young</surname><given-names>CS</given-names></name></person-group><year>2007</year><article-title>Simple scaling laws for influenza A rise time, duration, and severity.</article-title><source>J Theor Biol</source><volume>246</volume><fpage>621</fpage><lpage>635</lpage><pub-id pub-id-type="pmid">17379249</pub-id></element-citation></ref><ref id="pone.0011655-Brankston1"><label>44</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Brankston</surname><given-names>G</given-names></name><name><surname>Gitterman</surname><given-names>L</given-names></name><name><surname>Hirji</surname><given-names>Z</given-names></name><name><surname>Lemieux</surname><given-names>C</given-names></name><name><surname>Gardan</surname><given-names>M</given-names></name></person-group><year>2007</year><article-title>Transmission of influenza A in human beings.</article-title><source>Lancet Infect Dis</source><volume>7</volume><fpage>257</fpage><lpage>265</lpage><pub-id pub-id-type="pmid">17376383</pub-id></element-citation></ref><ref id="pone.0011655-Tellier1"><label>45</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tellier</surname><given-names>R</given-names></name></person-group><year>2009</year><article-title>Aerosol transmission of influenza A virus: a review of new studies.</article-title><source>J R Soc Interface</source><volume>6</volume><issue>Suppl 6</issue><fpage>S783</fpage><lpage>90</lpage><pub-id pub-id-type="pmid">19773292</pub-id></element-citation></ref><ref id="pone.0011655-Nicas1"><label>46</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nicas</surname><given-names>M</given-names></name><name><surname>Best</surname><given-names>D</given-names></name></person-group><year>2008</year><article-title>A Study Quantifying the Hand-to-Face Contact Rate and Its potential applications to predicting Respiratory tract infections.</article-title><source>J Occup Environ Hyg</source><volume>5</volume><fpage>347</fpage><lpage>352</lpage><pub-id pub-id-type="pmid">18357546</pub-id></element-citation></ref><ref id="pone.0011655-Mathews1"><label>47</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mathews</surname><given-names>JD</given-names></name><name><surname>Mccaw</surname><given-names>CT</given-names></name><name><surname>Mcvernon</surname><given-names>J</given-names></name><name><surname>Mcbryde</surname><given-names>ES</given-names></name><name><surname>Mccaw</surname><given-names>JM</given-names></name></person-group><year>2007</year><article-title>A Biological Model for Influenza Transmission : Pandemic Planning Implications of Asymptomatic Infection and Immunity.</article-title><source>PloS One</source><volume>2</volume><fpage>e1220</fpage><pub-id pub-id-type="pmid">18043733</pub-id></element-citation></ref><ref id="pone.0011655-Ferguson1"><label>48</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ferguson</surname><given-names>NM</given-names></name><name><surname>Cummings</surname><given-names>DAT</given-names></name><name><surname>Fraser</surname><given-names>C</given-names></name><name><surname>Cajka</surname><given-names>JC</given-names></name><name><surname>Cooley</surname><given-names>PC</given-names></name><etal></etal></person-group><year>2006</year><article-title>Strategies for mitigating an influenza pandemic.</article-title><source>Nature</source><volume>442</volume><fpage>448</fpage><lpage>452</lpage><pub-id pub-id-type="pmid">16642006</pub-id></element-citation></ref><ref id="pone.0011655-Halloran1"><label>49</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Halloran</surname><given-names>ME</given-names></name><name><surname>Ferguson</surname><given-names>NM</given-names></name><name><surname>Eubank</surname><given-names>S</given-names></name><name><surname>Longini</surname><given-names>IM</given-names></name><name><surname>Cummings</surname><given-names>DAT</given-names></name><etal></etal></person-group><year>2008</year><article-title>Modeling targeted layered containment of an influenza pandemic in the United States.</article-title><source>PNAS</source><volume>105</volume><fpage>4639</fpage><lpage>4644</lpage><pub-id pub-id-type="pmid">18332436</pub-id></element-citation></ref><ref id="pone.0011655-Andreasen1"><label>50</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Andreasen</surname><given-names>V</given-names></name><name><surname>Viboud</surname><given-names>C</given-names></name><name><surname>Simonsen</surname><given-names>L</given-names></name></person-group><year>2008</year><article-title>Epidemiologic characterization of the 1918 influenza pandemic summer wave in Copenhagen: implications for pandemic control strategies.</article-title><source>J Infect Dis</source><volume>197</volume><fpage>270</fpage><lpage>278</lpage><pub-id pub-id-type="pmid">18194088</pub-id></element-citation></ref><ref id="pone.0011655-Davies1"><label>51</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Davies</surname><given-names>JR</given-names></name><name><surname>Grilli</surname><given-names>EA</given-names></name><name><surname>Smith</surname><given-names>AJ</given-names></name></person-group><year>1984</year><article-title>Influenza A : infection and reinfection Influenza.</article-title><source>J Hyg (Lond)</source><volume>92</volume><fpage>125</fpage><lpage>127</lpage><pub-id pub-id-type="pmid">6693762</pub-id></element-citation></ref><ref id="pone.0011655-Grilli1"><label>52</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Grilli</surname><given-names>EA</given-names></name><name><surname>Davies</surname><given-names>JR</given-names></name><name><surname>Smith</surname><given-names>AJ</given-names></name></person-group><year>1986</year><article-title>Infection with influenza A H1N1. production and persistence of antibody.</article-title><source>J Hyg (Lond)</source><volume>96</volume><fpage>335</fpage><lpage>343</lpage><pub-id pub-id-type="pmid">3701045</pub-id></element-citation></ref><ref id="pone.0011655-Sonoguchi1"><label>53</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sonoguchi</surname><given-names>T</given-names></name><name><surname>Sakoh</surname><given-names>M</given-names></name><name><surname>Kunita</surname><given-names>N</given-names></name><name><surname>Satsuta</surname><given-names>K</given-names></name><name><surname>Fukumi</surname><given-names>H</given-names></name></person-group><year>1986</year><article-title>Reinfection with influenza A ( H2N2, H3N2, and H1N1 ) viruses in soldiers and students in Japan.</article-title><source>J Infect Dis</source><volume>153</volume><fpage>33</fpage><lpage>40</lpage><pub-id pub-id-type="pmid">3941288</pub-id></element-citation></ref><ref id="pone.0011655-Renshaw1"><label>54</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Renshaw</surname><given-names>E</given-names></name></person-group><year>1995</year><source>Modelling biological populations in space and time.</source><publisher-name>Cambridge University Press</publisher-name><size units="page">403</size></element-citation></ref><ref id="pone.0011655-Weber1"><label>55</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Weber</surname><given-names>TP</given-names></name><name><surname>Stilianakis</surname><given-names>NI</given-names></name></person-group><year>2008</year><article-title>Inactivation of influenza A viruses in the environment and modes of transmission: a critical review.</article-title><source>J Infect</source><volume>57</volume><fpage>361</fpage><lpage>373</lpage><pub-id pub-id-type="pmid">18848358</pub-id></element-citation></ref><ref id="pone.0011655-Shaman1"><label>56</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shaman</surname><given-names>J</given-names></name><name><surname>Kohn</surname><given-names>M</given-names></name></person-group><year>2009</year><article-title>Absolute humidity modulates influenza survival, transmission, and seasonality.</article-title><source>PNAS</source><volume>106</volume><fpage>3243</fpage><lpage>3248</lpage><pub-id pub-id-type="pmid">19204283</pub-id></element-citation></ref><ref id="pone.0011655-Lipsitch1"><label>57</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lipsitch</surname><given-names>M</given-names></name><name><surname>Viboud</surname><given-names>C</given-names></name></person-group><year>2009</year><article-title>Influenza seasonality: lifting the fog.</article-title><source>PNAS</source><volume>106</volume><fpage>3645</fpage><lpage>3646</lpage><pub-id pub-id-type="pmid">19276125</pub-id></element-citation></ref><ref id="pone.0011655-Vynnycky1"><label>58</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Vynnycky</surname><given-names>E</given-names></name><name><surname>Edmunds</surname><given-names>WJ</given-names></name></person-group><year>2008</year><article-title>Analyses of the 1957 ( Asian ) influenza pandemic in the United Kingdom and the impact of school closures.</article-title><source>Epidemiol Infect</source><volume>136</volume><fpage>166</fpage><lpage>179</lpage><pub-id pub-id-type="pmid">17445311</pub-id></element-citation></ref><ref id="pone.0011655-Dushoff1"><label>59</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dushoff</surname><given-names>J</given-names></name><name><surname>Plotkin</surname><given-names>JB</given-names></name><name><surname>Levin</surname><given-names>SA</given-names></name><name><surname>Earn</surname><given-names>DJD</given-names></name></person-group><year>2004</year><article-title>Dynamical resonance can account for seasonality of influenza epidemics.</article-title><source>PNAS</source><volume>101</volume><fpage>16915</fpage><lpage>16916</lpage><pub-id pub-id-type="pmid">15557003</pub-id></element-citation></ref><ref id="pone.0011655-Mills1"><label>60</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mills</surname><given-names>CE</given-names></name><name><surname>Robins</surname><given-names>JM</given-names></name><name><surname>Lipsitch</surname><given-names>M</given-names></name></person-group><year>2004</year><article-title>Transmissibility of 1918 pandemic influenza.</article-title><source>Nature</source><volume>432</volume><fpage>904</fpage><lpage>906</lpage><pub-id pub-id-type="pmid">15602562</pub-id></element-citation></ref><ref id="pone.0011655-White1"><label>61</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>White</surname><given-names>LF</given-names></name><name><surname>Pagano</surname><given-names>M</given-names></name></person-group><year>2008</year><article-title>Transmissibility of the influenza virus in the 1918 pandemic.</article-title><source>PLoS One</source><volume>3</volume><fpage>e1498</fpage><pub-id pub-id-type="pmid">18231585</pub-id></element-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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