Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases
Identifieur interne : 000E83 ( Pmc/Corpus ); précédent : 000E82; suivant : 000E84Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases
Auteurs : Keisuke Ejima ; Kazuyuki Aihara ; Hiroshi NishiuraSource :
- Journal of Theoretical Biology [ 0022-5193 ] ; 2014.
Abstract
Middle East respiratory syndrome (MERS) has spread worldwide since 2012. As the clinical symptoms of MERS tend to be non-specific, the incubation period has been shown to complement differential diagnosis, especially to rule out influenza. However, because an infection event is seldom directly observable, the present study aims to construct a diagnostic model that predicts the probability of MERS diagnosis given the time from immigration to illness onset among imported cases which are suspected of MERS. Addressing censoring by considering the transmission dynamics in an exporting country, we demonstrate that the illness onset within 2 days from immigration is suggestive of influenza. Two exceptions to suspect MERS even for those with illness onset within 2 days since immigration are (i) when we observe substantial community transmissions of MERS and (ii) when the cases are at high risk of MERS (e.g. cases with close contact in hospital or household). It is vital to collect the information of the incubation period upon emergence of a novel infectious disease, and moreover, in our model, the fundamental transmission dynamics including the initial growth rate has to be explored to differentiate the disease diagnoses with non-specific symptoms.
Url:
DOI: 10.1016/j.jtbi.2013.12.024
PubMed: 24406808
PubMed Central: 7094128
Links to Exploration step
PMC:7094128Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases</title><author><name sortKey="Ejima, Keisuke" sort="Ejima, Keisuke" uniqKey="Ejima K" first="Keisuke" last="Ejima">Keisuke Ejima</name><affiliation><nlm:aff id="aff0005">Graduate School of Medicine, The University of Tokyo, Medical Building No. 3, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan</nlm:aff></affiliation><affiliation><nlm:aff id="aff0010">Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan</nlm:aff></affiliation></author><author><name sortKey="Aihara, Kazuyuki" sort="Aihara, Kazuyuki" uniqKey="Aihara K" first="Kazuyuki" last="Aihara">Kazuyuki Aihara</name><affiliation><nlm:aff id="aff0010">Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan</nlm:aff></affiliation><affiliation><nlm:aff id="aff0015">Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan</nlm:aff></affiliation></author><author><name sortKey="Nishiura, Hiroshi" sort="Nishiura, Hiroshi" uniqKey="Nishiura H" first="Hiroshi" last="Nishiura">Hiroshi Nishiura</name><affiliation><nlm:aff id="aff0005">Graduate School of Medicine, The University of Tokyo, Medical Building No. 3, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan</nlm:aff></affiliation><affiliation><nlm:aff id="aff0020">PRESTO, Japan Science and Technology Agency, Saitama, Japan</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">24406808</idno><idno type="pmc">7094128</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7094128</idno><idno type="RBID">PMC:7094128</idno><idno type="doi">10.1016/j.jtbi.2013.12.024</idno><date when="2014">2014</date><idno type="wicri:Area/Pmc/Corpus">000E83</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000E83</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases</title><author><name sortKey="Ejima, Keisuke" sort="Ejima, Keisuke" uniqKey="Ejima K" first="Keisuke" last="Ejima">Keisuke Ejima</name><affiliation><nlm:aff id="aff0005">Graduate School of Medicine, The University of Tokyo, Medical Building No. 3, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan</nlm:aff></affiliation><affiliation><nlm:aff id="aff0010">Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan</nlm:aff></affiliation></author><author><name sortKey="Aihara, Kazuyuki" sort="Aihara, Kazuyuki" uniqKey="Aihara K" first="Kazuyuki" last="Aihara">Kazuyuki Aihara</name><affiliation><nlm:aff id="aff0010">Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan</nlm:aff></affiliation><affiliation><nlm:aff id="aff0015">Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan</nlm:aff></affiliation></author><author><name sortKey="Nishiura, Hiroshi" sort="Nishiura, Hiroshi" uniqKey="Nishiura H" first="Hiroshi" last="Nishiura">Hiroshi Nishiura</name><affiliation><nlm:aff id="aff0005">Graduate School of Medicine, The University of Tokyo, Medical Building No. 3, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan</nlm:aff></affiliation><affiliation><nlm:aff id="aff0020">PRESTO, Japan Science and Technology Agency, Saitama, Japan</nlm:aff></affiliation></author></analytic><series><title level="j">Journal of Theoretical Biology</title><idno type="ISSN">0022-5193</idno><idno type="eISSN">1095-8541</idno><imprint><date when="2014">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Middle East respiratory syndrome (MERS) has spread worldwide since 2012. As the clinical symptoms of MERS tend to be non-specific, the incubation period has been shown to complement differential diagnosis, especially to rule out influenza. However, because an infection event is seldom directly observable, the present study aims to construct a diagnostic model that predicts the probability of MERS diagnosis given the time from immigration to illness onset among imported cases which are suspected of MERS. Addressing censoring by considering the transmission dynamics in an exporting country, we demonstrate that the illness onset within 2 days from immigration is suggestive of influenza. Two exceptions to suspect MERS even for those with illness onset within 2 days since immigration are (i) when we observe substantial community transmissions of MERS and (ii) when the cases are at high risk of MERS (e.g. cases with close contact in hospital or household). It is vital to collect the information of the incubation period upon emergence of a novel infectious disease, and moreover, in our model, the fundamental transmission dynamics including the initial growth rate has to be explored to differentiate the disease diagnoses with non-specific symptoms.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Assiri, A" uniqKey="Assiri A">A. Assiri</name></author><author><name sortKey="Al Tawfiq, J A" uniqKey="Al Tawfiq J">J.A. Al-Tawfiq</name></author><author><name sortKey="Al Rabeeah, A A" uniqKey="Al Rabeeah A">A.A. Al-Rabeeah</name></author><author><name sortKey="Al Rabiah, F A" uniqKey="Al Rabiah F">F.A. Al-Rabiah</name></author><author><name sortKey="Al Hajjar, S" uniqKey="Al Hajjar S">S. Al-Hajjar</name></author><author><name sortKey="Al Barrak, A" uniqKey="Al Barrak A">A. Al-Barrak</name></author><author><name sortKey="Flemban, H" uniqKey="Flemban H">H. Flemban</name></author><author><name sortKey="Al Nassir, W N" uniqKey="Al Nassir W">W.N. Al-Nassir</name></author><author><name sortKey="Balkhy, H H" uniqKey="Balkhy H">H.H. Balkhy</name></author><author><name sortKey="Al Hakeem, R F" uniqKey="Al Hakeem R">R.F. Al-Hakeem</name></author><author><name sortKey="Makhdoom, H Q" uniqKey="Makhdoom H">H.Q. Makhdoom</name></author><author><name sortKey="Zumla, A I" uniqKey="Zumla A">A.I. Zumla</name></author><author><name sortKey="Memish, Z A" uniqKey="Memish Z">Z.A. Memish</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Assiri, A" uniqKey="Assiri A">A. Assiri</name></author><author><name sortKey="Mcgeer, A" uniqKey="Mcgeer A">A. McGeer</name></author><author><name sortKey="Perl, T M" uniqKey="Perl T">T.M. Perl</name></author><author><name sortKey="Price, C S" uniqKey="Price C">C.S. Price</name></author><author><name sortKey="Al Rabeeah, A A" uniqKey="Al Rabeeah A">A.A. Al Rabeeah</name></author><author><name sortKey="Cummings, D A" uniqKey="Cummings D">D.A. Cummings</name></author><author><name sortKey="Alabdullatif, Z N" uniqKey="Alabdullatif Z">Z.N. Alabdullatif</name></author><author><name sortKey="Assad, M" uniqKey="Assad M">M. Assad</name></author><author><name sortKey="Almulhim, A" uniqKey="Almulhim A">A. Almulhim</name></author><author><name sortKey="Makhdoom, H" uniqKey="Makhdoom H">H. Makhdoom</name></author><author><name sortKey="Madani, H" uniqKey="Madani H">H. Madani</name></author><author><name sortKey="Alhakeem, R" uniqKey="Alhakeem R">R. Alhakeem</name></author><author><name sortKey="Al Tawfiq, J A" uniqKey="Al Tawfiq J">J.A. Al-Tawfiq</name></author><author><name sortKey="Cotten, M" uniqKey="Cotten M">M. Cotten</name></author><author><name sortKey="Watson, S J" uniqKey="Watson S">S.J. Watson</name></author><author><name sortKey="Kellam, P" uniqKey="Kellam P">P. Kellam</name></author><author><name sortKey="Zumla, A I" uniqKey="Zumla A">A.I. Zumla</name></author><author><name sortKey="Memish, Z A" uniqKey="Memish Z">Z.A. Memish</name></author><author><name sortKey="Mers Cov, K S A" uniqKey="Mers Cov K">K.S.A. MERS-CoV</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Breban, R" uniqKey="Breban R">R. Breban</name></author><author><name sortKey="Riou, J" uniqKey="Riou J">J. Riou</name></author><author><name sortKey="Fontanet, A" uniqKey="Fontanet A">A. Fontanet</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cauchemez, S" uniqKey="Cauchemez S">S. Cauchemez</name></author><author><name sortKey="Van Kerkhove, M D" uniqKey="Van Kerkhove M">M.D. Van Kerkhove</name></author><author><name sortKey="Riley, S" uniqKey="Riley S">S. Riley</name></author><author><name sortKey="Donnelly, C A" uniqKey="Donnelly C">C.A. Donnelly</name></author><author><name sortKey="Fraser, C" uniqKey="Fraser C">C. Fraser</name></author><author><name sortKey="Ferguson, N M" uniqKey="Ferguson N">N.M. Ferguson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cauchemez, S" uniqKey="Cauchemez S">S. Cauchemez</name></author><author><name sortKey="Fraser, C" uniqKey="Fraser C">C. Fraser</name></author><author><name sortKey="Van Kerkhove, M D" uniqKey="Van Kerkhove M">M.D. Van Kerkhove</name></author><author><name sortKey="Donnelly, C A" uniqKey="Donnelly C">C.A. Donnelly</name></author><author><name sortKey="Riley, S" uniqKey="Riley S">S. Riley</name></author><author><name sortKey="Rambaut, A" uniqKey="Rambaut A">A. Rambaut</name></author><author><name sortKey="Enouf, V" uniqKey="Enouf V">V. Enouf</name></author><author><name sortKey="Van Der Werf, S" uniqKey="Van Der Werf S">S. van der Werf</name></author><author><name sortKey="Ferguson, N M" uniqKey="Ferguson N">N.M. Ferguson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Clancy, D" uniqKey="Clancy D">D. Clancy</name></author><author><name sortKey="O Eill, P D" uniqKey="O Eill P">P.D. O’Neill</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cotten, M" uniqKey="Cotten M">M. Cotten</name></author><author><name sortKey="Watson, S J" uniqKey="Watson S">S.J. Watson</name></author><author><name sortKey="Kellam, P" uniqKey="Kellam P">P. Kellam</name></author><author><name sortKey="Al Rabeeah, A A" uniqKey="Al Rabeeah A">A.A. Al-Rabeeah</name></author><author><name sortKey="Makhdoom, H Q" uniqKey="Makhdoom H">H.Q. Makhdoom</name></author><author><name sortKey="Assiri, A" uniqKey="Assiri A">A. Assiri</name></author><author><name sortKey="Al Tawfiq, J A" uniqKey="Al Tawfiq J">J.A. Al-Tawfiq</name></author><author><name sortKey="Alhakeem, R F" uniqKey="Alhakeem R">R.F. Alhakeem</name></author><author><name sortKey="Madani, H" uniqKey="Madani H">H. Madani</name></author><author><name sortKey="Alrabiah, F A" uniqKey="Alrabiah F">F.A. AlRabiah</name></author><author><name sortKey="Al Hajjar, S" uniqKey="Al Hajjar S">S. Al Hajjar</name></author><author><name sortKey="Al Nassir, W N" uniqKey="Al Nassir W">W.N. Al-nassir</name></author><author><name sortKey="Albarrak, A" uniqKey="Albarrak A">A. Albarrak</name></author><author><name sortKey="Flemban, H" uniqKey="Flemban H">H. Flemban</name></author><author><name sortKey="Balkhy, H H" uniqKey="Balkhy H">H.H. Balkhy</name></author><author><name sortKey="Alsubaie, S" uniqKey="Alsubaie S">S. Alsubaie</name></author><author><name sortKey="Palser, A L" uniqKey="Palser A">A.L. Palser</name></author><author><name sortKey="Gall, A" uniqKey="Gall A">A. Gall</name></author><author><name sortKey="Bashford Rogers, R" uniqKey="Bashford Rogers R">R. Bashford-Rogers</name></author><author><name sortKey="Rambaut, A" uniqKey="Rambaut A">A. Rambaut</name></author><author><name sortKey="Zumla, A I" uniqKey="Zumla A">A.I. Zumla</name></author><author><name sortKey="Memish, Z A" uniqKey="Memish Z">Z.A. Memish</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="De Wit, E" uniqKey="De Wit E">E. de Wit</name></author><author><name sortKey="Rasmussen, A L" uniqKey="Rasmussen A">A.L. Rasmussen</name></author><author><name sortKey="Falzarano, D" uniqKey="Falzarano D">D. Falzarano</name></author><author><name sortKey="Bushmaker, T" uniqKey="Bushmaker T">T. Bushmaker</name></author><author><name sortKey="Feldmann, F" uniqKey="Feldmann F">F. Feldmann</name></author><author><name sortKey="Brining, D L" uniqKey="Brining D">D.L. Brining</name></author><author><name sortKey="Fischer, E R" uniqKey="Fischer E">E.R. Fischer</name></author><author><name sortKey="Martellaro, C" uniqKey="Martellaro C">C. Martellaro</name></author><author><name sortKey="Okumura, A" uniqKey="Okumura A">A. Okumura</name></author><author><name sortKey="Chang, J" uniqKey="Chang J">J. Chang</name></author><author><name sortKey="Scott, D" uniqKey="Scott D">D. Scott</name></author><author><name sortKey="Benecke, A G" uniqKey="Benecke A">A.G. Benecke</name></author><author><name sortKey="Katze, M G" uniqKey="Katze M">M.G. Katze</name></author><author><name sortKey="Feldmann, H" uniqKey="Feldmann H">H. Feldmann</name></author><author><name sortKey="Munster, V J" uniqKey="Munster V">V.J. Munster</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Donnelly, C A" uniqKey="Donnelly C">C.A. Donnelly</name></author><author><name sortKey="Ghani, A C" uniqKey="Ghani A">A.C. Ghani</name></author><author><name sortKey="Leung, G M" uniqKey="Leung G">G.M. Leung</name></author><author><name sortKey="Hedley, A J" uniqKey="Hedley A">A.J. Hedley</name></author><author><name sortKey="Fraser, C" uniqKey="Fraser C">C. Fraser</name></author><author><name sortKey="Riley, S" uniqKey="Riley S">S. Riley</name></author><author><name sortKey="Abu Raddad, L J" uniqKey="Abu Raddad L">L.J. Abu-Raddad</name></author><author><name sortKey="Ho, L M" uniqKey="Ho L">L.M. Ho</name></author><author><name sortKey="Thach, T Q" uniqKey="Thach T">T.Q. Thach</name></author><author><name sortKey="Chau, P" uniqKey="Chau P">P. Chau</name></author><author><name sortKey="Chan, K P" uniqKey="Chan K">K.P. Chan</name></author><author><name sortKey="Lam, T H" uniqKey="Lam T">T.H. Lam</name></author><author><name sortKey="Tse, L Y" uniqKey="Tse L">L.Y. Tse</name></author><author><name sortKey="Tsang, T" uniqKey="Tsang T">T. Tsang</name></author><author><name sortKey="Liu, S H" uniqKey="Liu S">S.H. Liu</name></author><author><name sortKey="Kong, J H" uniqKey="Kong J">J.H. Kong</name></author><author><name sortKey="Lau, E M" uniqKey="Lau E">E.M. Lau</name></author><author><name sortKey="Ferguson, N M" uniqKey="Ferguson N">N.M. Ferguson</name></author><author><name sortKey="Anderson, R M" uniqKey="Anderson R">R.M. Anderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ejima, K" uniqKey="Ejima K">K. Ejima</name></author><author><name sortKey="Aihara, K" uniqKey="Aihara K">K. Aihara</name></author><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Fisman, D N" uniqKey="Fisman D">D.N. Fisman</name></author><author><name sortKey="Tuite, A R" uniqKey="Tuite A">A.R. Tuite</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Guery, B" uniqKey="Guery B">B. Guery</name></author><author><name sortKey="Poissy, J" uniqKey="Poissy J">J. Poissy</name></author><author><name sortKey="El Mansouf, L" uniqKey="El Mansouf L">L. el Mansouf</name></author><author><name sortKey="Sejourne, C" uniqKey="Sejourne C">C. Séjourné</name></author><author><name sortKey="Ettahar, N" uniqKey="Ettahar N">N. Ettahar</name></author><author><name sortKey="Lemaire, X" uniqKey="Lemaire X">X. Lemaire</name></author><author><name sortKey="Vuotto, F" uniqKey="Vuotto F">F. Vuotto</name></author><author><name sortKey="Goffard, A" uniqKey="Goffard A">A. Goffard</name></author><author><name sortKey="Behillil, S" uniqKey="Behillil S">S. Behillil</name></author><author><name sortKey="Enouf, V" uniqKey="Enouf V">V. Enouf</name></author><author><name sortKey="Caro, V" uniqKey="Caro V">V. Caro</name></author><author><name sortKey="Mailles, A" uniqKey="Mailles A">A. Mailles</name></author><author><name sortKey="Che, D" uniqKey="Che D">D. Che</name></author><author><name sortKey="Manuguerra, J C" uniqKey="Manuguerra J">J.C. Manuguerra</name></author><author><name sortKey="Mathieu, D" uniqKey="Mathieu D">D. Mathieu</name></author><author><name sortKey="Fontanet, A" uniqKey="Fontanet A">A. Fontanet</name></author><author><name sortKey="Van Der Werf, S" uniqKey="Van Der Werf S">S. van der Werf</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Klinkenberg, D" uniqKey="Klinkenberg D">D. Klinkenberg</name></author><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lam, E H" uniqKey="Lam E">E.H. Lam</name></author><author><name sortKey="Cowling, B J" uniqKey="Cowling B">B.J. Cowling</name></author><author><name sortKey="Cook, A R" uniqKey="Cook A">A.R. Cook</name></author><author><name sortKey="Wong, J Y" uniqKey="Wong J">J.Y. Wong</name></author><author><name sortKey="Lau, M S" uniqKey="Lau M">M.S. Lau</name></author><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lessler, J" uniqKey="Lessler J">J. Lessler</name></author><author><name sortKey="Brookmeyer, R" uniqKey="Brookmeyer R">R. Brookmeyer</name></author><author><name sortKey="Perl, T M" uniqKey="Perl T">T.M. Perl</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lessler, J" uniqKey="Lessler J">J. Lessler</name></author><author><name sortKey="Brookmeyer, R" uniqKey="Brookmeyer R">R. Brookmeyer</name></author><author><name sortKey="Reich, N G" uniqKey="Reich N">N.G. Reich</name></author><author><name sortKey="Nelson, K E" uniqKey="Nelson K">K.E. Nelson</name></author><author><name sortKey="Cummings, D A" uniqKey="Cummings D">D.A. Cummings</name></author><author><name sortKey="Perl, T M" uniqKey="Perl T">T.M. Perl</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author><author><name sortKey="Inaba, H" uniqKey="Inaba H">H. Inaba</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author><author><name sortKey="Kamiya, K" uniqKey="Kamiya K">K. Kamiya</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author><author><name sortKey="Mizumoto, K" uniqKey="Mizumoto K">K. Mizumoto</name></author><author><name sortKey="Ejima, K" uniqKey="Ejima K">K. Ejima</name></author><author><name sortKey="Zhong, Y" uniqKey="Zhong Y">Y. Zhong</name></author><author><name sortKey="Cowling, B" uniqKey="Cowling B">B. Cowling</name></author><author><name sortKey="Omori, R" uniqKey="Omori R">R. Omori</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author><author><name sortKey="Mizumoto, K" uniqKey="Mizumoto K">K. Mizumoto</name></author><author><name sortKey="Ejima, K" uniqKey="Ejima K">K. Ejima</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nishiura, H" uniqKey="Nishiura H">H. Nishiura</name></author><author><name sortKey="Ejima, K" uniqKey="Ejima K">K. Ejima</name></author><author><name sortKey="Mizumoto, K" uniqKey="Mizumoto K">K. Mizumoto</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Reich, N G" uniqKey="Reich N">N.G. Reich</name></author><author><name sortKey="Lessler, J" uniqKey="Lessler J">J. Lessler</name></author><author><name sortKey="Cummings, D A" uniqKey="Cummings D">D.A. Cummings</name></author><author><name sortKey="Brookmeyer, R" uniqKey="Brookmeyer R">R. Brookmeyer</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Reusken, C" uniqKey="Reusken C">C. Reusken</name></author><author><name sortKey="Ababneh, M" uniqKey="Ababneh M">M. Ababneh</name></author><author><name sortKey="Raj, V" uniqKey="Raj V">V. Raj</name></author><author><name sortKey="Meyer, B" uniqKey="Meyer B">B. Meyer</name></author><author><name sortKey="Eljarah, A" uniqKey="Eljarah A">A. Eljarah</name></author><author><name sortKey="Abutarbush, S" uniqKey="Abutarbush S">S. Abutarbush</name></author><author><name sortKey="Godeke, G" uniqKey="Godeke G">G. Godeke</name></author><author><name sortKey="Bestebroer, T" uniqKey="Bestebroer T">T. Bestebroer</name></author><author><name sortKey="Zutt, I" uniqKey="Zutt I">I. Zutt</name></author><author><name sortKey="Muller, M" uniqKey="Muller M">M. Muller</name></author><author><name sortKey="Bosch, B" uniqKey="Bosch B">B. Bosch</name></author><author><name sortKey="Rottier, P" uniqKey="Rottier P">P. Rottier</name></author><author><name sortKey="Osterhaus, A" uniqKey="Osterhaus A">A. Osterhaus</name></author><author><name sortKey="Drosten, C" uniqKey="Drosten C">C. Drosten</name></author><author><name sortKey="Haagmans, B" uniqKey="Haagmans B">B. Haagmans</name></author><author><name sortKey="Koopmans, M" uniqKey="Koopmans M">M. Koopmans</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Reusken, C B" uniqKey="Reusken C">C.B. Reusken</name></author><author><name sortKey="Haagmans, B L" uniqKey="Haagmans B">B.L. Haagmans</name></author><author><name sortKey="Muller, M A" uniqKey="Muller M">M.A. Müller</name></author><author><name sortKey="Gutierrez, C" uniqKey="Gutierrez C">C. Gutierrez</name></author><author><name sortKey="Godeke, G J" uniqKey="Godeke G">G.J. Godeke</name></author><author><name sortKey="Meyer, B" uniqKey="Meyer B">B. Meyer</name></author><author><name sortKey="Muth, D" uniqKey="Muth D">D. Muth</name></author><author><name sortKey="Raj, V S" uniqKey="Raj V">V.S. Raj</name></author><author><name sortKey="Smits De Vries, L" uniqKey="Smits De Vries L">L. Smits-De Vries</name></author><author><name sortKey="Corman, V M" uniqKey="Corman V">V.M. Corman</name></author><author><name sortKey="Drexler, J F" uniqKey="Drexler J">J.F. Drexler</name></author><author><name sortKey="Smits, S L" uniqKey="Smits S">S.L. Smits</name></author><author><name sortKey="El Tahir, Y E" uniqKey="El Tahir Y">Y.E. El Tahir</name></author><author><name sortKey="De Sousa, R" uniqKey="De Sousa R">R. De Sousa</name></author><author><name sortKey="Van Beek, J" uniqKey="Van Beek J">J. van Beek</name></author><author><name sortKey="Nowotny, N" uniqKey="Nowotny N">N. Nowotny</name></author><author><name sortKey="Van Maanen, K" uniqKey="Van Maanen K">K. van Maanen</name></author><author><name sortKey="Hidalgo Hermoso, E" uniqKey="Hidalgo Hermoso E">E. Hidalgo-Hermoso</name></author><author><name sortKey="Bosch, B J" uniqKey="Bosch B">B.J. Bosch</name></author><author><name sortKey="Rottier, P" uniqKey="Rottier P">P. Rottier</name></author><author><name sortKey="Osterhaus, A" uniqKey="Osterhaus A">A. Osterhaus</name></author><author><name sortKey="Gortazar Schmidt, C" uniqKey="Gortazar Schmidt C">C. Gortázar-Schmidt</name></author><author><name sortKey="Drosten, C" uniqKey="Drosten C">C. Drosten</name></author><author><name sortKey="Koopmans, M P" uniqKey="Koopmans M">M.P. Koopmans</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Roberts, M G" uniqKey="Roberts M">M.G. Roberts</name></author><author><name sortKey="Heesterbeek, J A" uniqKey="Heesterbeek J">J.A. Heesterbeek</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Wallinga, J" uniqKey="Wallinga J">J. Wallinga</name></author><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M. Lipsitch</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">J Theor Biol</journal-id><journal-id journal-id-type="iso-abbrev">J. Theor. Biol</journal-id><journal-title-group><journal-title>Journal of Theoretical Biology</journal-title></journal-title-group><issn pub-type="ppub">0022-5193</issn><issn pub-type="epub">1095-8541</issn><publisher><publisher-name>Elsevier Ltd.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">24406808</article-id><article-id pub-id-type="pmc">7094128</article-id><article-id pub-id-type="publisher-id">S0022-5193(13)00589-4</article-id><article-id pub-id-type="doi">10.1016/j.jtbi.2013.12.024</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases</article-title></title-group><contrib-group><contrib contrib-type="author" id="au0005"><name><surname>Ejima</surname><given-names>Keisuke</given-names></name><xref rid="aff0005" ref-type="aff">a</xref><xref rid="aff0010" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au0010"><name><surname>Aihara</surname><given-names>Kazuyuki</given-names></name><xref rid="aff0010" ref-type="aff">b</xref><xref rid="aff0015" ref-type="aff">c</xref></contrib><contrib contrib-type="author" id="au0015"><name><surname>Nishiura</surname><given-names>Hiroshi</given-names></name><email>nishiurah@m.u-tokyo.ac.jp</email><xref rid="aff0005" ref-type="aff">a</xref><xref rid="aff0020" ref-type="aff">d</xref><xref rid="cor1" ref-type="corresp">⁎</xref></contrib></contrib-group><aff id="aff0005"><label>a</label>Graduate School of Medicine, The University of Tokyo, Medical Building No. 3, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan</aff><aff id="aff0010"><label>b</label>Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan</aff><aff id="aff0015"><label>c</label>Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan</aff><aff id="aff0020"><label>d</label>PRESTO, Japan Science and Technology Agency, Saitama, Japan</aff><author-notes><corresp id="cor1"><label>⁎</label>Corresponding author at: Graduate School of Medicine, The University of Tokyo, Medical Building No. 3, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.Tel: +81 3 5841 3688; fax: +81 3 5841 3637. <email>nishiurah@m.u-tokyo.ac.jp</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>6</day><month>1</month><year>2014</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on .</pmc-comment>
<pub-date pub-type="ppub"><day>7</day><month>4</month><year>2014</year></pub-date><pub-date pub-type="epub"><day>6</day><month>1</month><year>2014</year></pub-date><volume>346</volume><fpage>47</fpage><lpage>53</lpage><history><date date-type="received"><day>24</day><month>12</month><year>2012</year></date><date date-type="rev-recd"><day>25</day><month>12</month><year>2013</year></date><date date-type="accepted"><day>26</day><month>12</month><year>2013</year></date></history><permissions><copyright-statement>Copyright © 2014 Elsevier Ltd. All rights reserved.</copyright-statement><copyright-year>2014</copyright-year><copyright-holder>Elsevier Ltd</copyright-holder><license><license-p>Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.</license-p></license></permissions><abstract id="ab0005"><p>Middle East respiratory syndrome (MERS) has spread worldwide since 2012. As the clinical symptoms of MERS tend to be non-specific, the incubation period has been shown to complement differential diagnosis, especially to rule out influenza. However, because an infection event is seldom directly observable, the present study aims to construct a diagnostic model that predicts the probability of MERS diagnosis given the time from immigration to illness onset among imported cases which are suspected of MERS. Addressing censoring by considering the transmission dynamics in an exporting country, we demonstrate that the illness onset within 2 days from immigration is suggestive of influenza. Two exceptions to suspect MERS even for those with illness onset within 2 days since immigration are (i) when we observe substantial community transmissions of MERS and (ii) when the cases are at high risk of MERS (e.g. cases with close contact in hospital or household). It is vital to collect the information of the incubation period upon emergence of a novel infectious disease, and moreover, in our model, the fundamental transmission dynamics including the initial growth rate has to be explored to differentiate the disease diagnoses with non-specific symptoms.</p></abstract><abstract abstract-type="author-highlights" id="ab0010"><title>Highlights</title><p><list list-type="simple" id="li0005"><list-item id="u0005"><label>•</label><p id="p0005">Clinical symptoms of MERS tend to be non-specific.</p></list-item><list-item id="u0010"><label>•</label><p id="p0010">The incubation period complements differential diagnosis, ruling out influenza.</p></list-item><list-item id="u0015"><label>•</label><p id="p0015">The time from immigration to illness in imported cases also informs diagnosis.</p></list-item><list-item id="u0020"><label>•</label><p id="p0020">Illness onset within 2 days from immigration is suggestive of influenza.</p></list-item></list></p></abstract><kwd-group id="keys0005"><title>Keywords</title><kwd>Importation</kwd><kwd>Epidemiology</kwd><kwd>Coronavirus</kwd><kwd>Mathematical model</kwd><kwd>Incubation period</kwd></kwd-group></article-meta></front><body><sec id="s0005"><label>1</label><title>Introduction</title><p id="p0025">Middle East respiratory syndrome (MERS), caused by the novel MERS coronavirus (MERS-CoV), has been reported since March 2012 (<xref rid="bib1" ref-type="bibr">Cauchemez et al., 2014</xref>). MERS-CoV has not caused substantial human-to-human transmissions yet, but the extent of geographic distribution of this disease has gradually expanded from Middle East countries (e.g. Jordan and Saudi Arabia) to other countries, including Europe. Recent studies have suggested that mildly symptomatic cases are common (<xref rid="bib1" ref-type="bibr">Cauchemez et al., 2014</xref>, <xref rid="bib2" ref-type="bibr">Fisman and Tuite, 2014</xref>, <xref rid="bib3" ref-type="bibr">Assiri et al., 2013a</xref>), while hospitalized cases tended to exhibit severe respiratory symptoms (<xref rid="bib4" ref-type="bibr">Assiri et al., 2013b</xref>, <xref rid="bib5" ref-type="bibr">, 2013</xref>).</p><p id="p0030">In October 2012, a Saudi boy was suspected of MERS in Hong Kong and was admitted to a hospital which is equipped with an isolation ward (<xref rid="bib6" ref-type="bibr">South China Morning Post, 2012</xref>). Two days in advance, his father had developed fever and coughing, and the boy followed similar symptoms to his father. One day after admission to the hospital in Hong Kong, the boy was tested positive to influenza A (H1N1) virus, while testing negative to MERS-CoV. The similar suspected cases caused by influenza have been also reported from other countries (<xref rid="bib7" ref-type="bibr">Nishiura et al., 2012</xref>). Not only influenza but also many other respiratory viruses induce only non-specific clinical signs and symptoms. Thus, it is difficult to selectively detect and differentially diagnose only MERS among imported cases with upper respiratory symptoms (e.g. by screening febrile individuals at an international border (<xref rid="bib8" ref-type="bibr">Nishiura and Kamiya, 2011</xref>)). Laboratory diagnosis such as PCR takes time and cost, and there would be a substantial number of suspected imported cases to be tested and isolated in hospital if we intend to test and intervene all suspected febrile individuals arriving from affected countries.</p><p id="p0035">As complimentary information to partly resolve this problem, a probabilistic model has been proposed to help differential diagnosis based on a known incubation period (<xref rid="bib7" ref-type="bibr">Nishiura et al., 2012</xref>). Employing a Bayesian approach, and assuming that the incubation period distribution and the prior probability (or the population risks) of all suspected respiratory viruses are known, the model has permitted us to calculate the probability of MERS given a certain length of the incubation period. Nevertheless, it has been recognized as a core issue of infectious disease epidemiology that an infection event of non-sexual directly transmitted diseases is seldom directly observable (<xref rid="bib9" ref-type="bibr">Clancy and O’Neill, 2008</xref>). Thus, the exact length of the incubation period is seldom known for each individual case. Nevertheless, it is frequently the case that the time of illness onset is remembered among cases, and the time from immigration to illness onset among imported cases is readily available and can be useful for demonstrating the practical usefulness of the probabilistic model to assist clinical diagnosis.</p><p id="p0040">The present study aims to construct a statistical model that predicts the probability of MERS diagnosis given a certain length of the time from immigration to illness onset among imported cases. Through this exercise, we also aim to assess practical and theoretical importance of the proposed model and identify associated data gaps in epidemiological observations.</p></sec><sec id="s0010"><label>2</label><title>Materials and methods</title><sec id="s0015"><label>2.1</label><title>Epidemiological setting</title><p id="p0045">Further to the present study, <xref rid="bib10" ref-type="bibr">Nishiura and Inaba (2011)</xref> proposed an estimation framework of the incubation period based on the time from immigration to illness onset among imported cases of influenza A (H1N1-2009) in Japan. While that study aimed to estimate the incubation period distribution, the present study extends the model structure in the earlier study to predict the probability of MERS diagnosis. In particular, the present study focuses on the distinction between influenza and MERS. During the early stages of the epidemic, the epidemiological parameters of MERS had yet to be estimated based on the empirical data. Thus, we also examine the corresponding estimates of the severe acute respiratory syndrome (SARS) as a substitute for MERS during the early stages.</p><p id="p0050">Let <italic>t</italic> be the time from immigration to illness onset in an imported case which developed a disease in country B at time <italic>t</italic>≥0 (where <italic>t</italic>=0 stands for the time of immigration;
<xref rid="f0005" ref-type="fig">Fig. 1</xref>). Suppose that he or she traveled to country A (where MERS has spread) for <italic>k</italic> days. In the case of resident of country A, we may drop the data or assume that <italic>k</italic>→∞. We consider two different patterns of spread in country A: (i) an endemic state (i.e. the risk of infection is in a stationary state) and (ii) an epidemic state. In the case of the latter, we assume that the epidemic of novel coronavirus is in an early stage with an approximately exponential growth of infections. The frequency of exposure among imported cases during their travel is assumed as proportional to the incidence in country A. The exponential growth rate of incidence is known to be characterized by the basic reproduction number <italic>R</italic><sub>0</sub> and the mean generation time <italic>T</italic><sub><italic>g</italic></sub> (<xref rid="bib11" ref-type="bibr">Wallinga and Lipsitch, 2007</xref>). If the generation time is exponentially distributed, the growth rate <italic>r</italic> is calculated as <italic>r</italic>=(<italic>R</italic><sub>0</sub>−1)/<italic>T</italic><sub><italic>g</italic></sub>, while we have <italic>r</italic>=ln(<italic>R</italic><sub>0</sub>)/<italic>T</italic><sub><italic>g</italic></sub> for a constant generation time (<xref rid="bib11" ref-type="bibr">Wallinga and Lipsitch, 2007</xref>). Given identical values of <italic>R</italic><sub>0</sub> and <italic>T</italic><sub><italic>g</italic></sub>, the exponential distribution is known to yield the largest value of <italic>r</italic> among all the possible distributions of the generation time, while a constant <italic>T</italic><sub><italic>g</italic></sub> gives the smallest <italic>r</italic> (<xref rid="bib12" ref-type="bibr">Roberts and Heesterbeek, 2007</xref>).<fig id="f0005"><label>Fig. 1</label><caption><p>Predicting influenza among imported cases based on the time since immigration. The mechanism and timing of importation: spending <italic>k</italic> days for travel, an exposure occurs in country A with a risk proportional to the incidence. Entering country B, the exposed individual develops illness at <italic>t</italic> days since immigration. Since an infection event is not directly observable, the exact length of the incubation period has to be inferred by addressing censoring and using an explicitly infection-age structured model.</p></caption><graphic xlink:href="gr1_lrg"></graphic></fig></p><p id="p0055">Here we briefly describe the time from immigration to illness onset among imported cases (<xref rid="bib10" ref-type="bibr">Nishiura and Inaba, 2011</xref>). Let <italic>i</italic>(<italic>t</italic>,<italic>τ</italic>) be the number of incubating individuals at time <italic>t</italic> after immigration and at infection-age <italic>τ</italic> (i.e. the time since infection). Supposing that the rate of illness onset at infection-age <italic>τ</italic> is <italic>γ</italic>(<italic>τ</italic>), the dynamics of the density of incubating individuals are described by<disp-formula id="eq0005"><label>(1)</label><mml:math id="M1" altimg="si0001.gif" overflow="scroll"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>τ</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:math></disp-formula>with boundary conditions<disp-formula id="eq0010"><label>(2)</label><mml:math id="M2" altimg="si0002.gif" overflow="scroll"><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mspace width="1em"></mml:mspace><mml:mtext>for</mml:mtext><mml:mspace width=".25em"></mml:mspace><mml:mi>t</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:math></disp-formula>here <italic>j</italic>(<italic>τ</italic>)=<italic>i</italic>(0,<italic>τ</italic>) represents the density of incubating population at an infection-age <italic>τ</italic> at the time of immigration <italic>t</italic>=0 (i.e. the initial age distribution). <italic>i</italic>(<italic>t</italic>,<italic>τ</italic>) can be integrated as<disp-formula id="eq0015"><label>(3)</label><mml:math id="M3" altimg="si0003.gif" overflow="scroll"><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>−</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mfrac><mml:mrow><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>−</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:math></disp-formula>for <italic>τ</italic>−<italic>t</italic>>0, where <italic>L</italic>(<italic>τ</italic>) represents the survival probability of incubating individuals at infection-age <italic>τ</italic>. The survival probability is calculated by using the rate of illness onset at infection-age <italic>τ</italic>, <italic>γ</italic>(<italic>τ</italic>) as follows:<disp-formula id="eq0020"><label>(4)</label><mml:math id="M4" altimg="si0004.gif" overflow="scroll"><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>exp</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>τ</mml:mi></mml:msubsup><mml:mrow><mml:mi>γ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>d</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>and, based on survival analysis, the probability density of the incubation period <italic>f</italic>(<italic>τ</italic>) is given as<disp-formula id="eq0025"><label>(5)</label><mml:math id="M5" altimg="si0005.gif" overflow="scroll"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:math></disp-formula></p><p id="p0075">Note that <italic>L</italic>(<italic>τ</italic>) is also written as 1−<italic>F</italic>(<italic>τ</italic>) where <italic>F</italic>(<italic>τ</italic>) is the cumulative distribution of the incubation period. Let <italic>c</italic>(<italic>t</italic>) be the number of new symptomatic cases (illness onsets) at time <italic>t</italic> after immigration. Supposing that the duration of travel is <italic>k</italic> days, then<disp-formula id="eq0030"><label>(6)</label><mml:math id="M6" altimg="si0006.gif" overflow="scroll"><mml:mi>c</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mi>t</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>γ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>d</mml:mi><mml:mi>τ</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mi>t</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>γ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mfrac><mml:mrow><mml:mi>j</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>−</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>−</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mi>d</mml:mi><mml:mi>τ</mml:mi></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>which can be rearranged as<disp-formula id="eq0035"><label>(7)</label><mml:math id="M7" altimg="si0007.gif" overflow="scroll"><mml:mi>c</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>k</mml:mi></mml:msubsup><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mfrac><mml:mrow><mml:mi>j</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mi>d</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:math></disp-formula>The frequency of illness onset is obtained by normalizing <italic>c</italic>(<italic>t</italic>) over <italic>t</italic>.</p></sec><sec id="s0020"><label>2.2</label><title>Statistical model</title><p id="p0090">Hereafter, we focus on differential diagnosis of two specific diseases, influenza and MERS. Suppose that both diseases are growing in a similar manner (i.e., both in an endemic state or both in an exponential growth phase with different growth rates due to different <italic>R</italic><sub>0</sub> and <italic>T</italic><sub><italic>g</italic></sub>). As was discussed by <xref rid="bib10" ref-type="bibr">Nishiura and Inaba (2011)</xref>, the frequency of exposure in an epidemic case is written as<disp-formula id="eq0040"><label>(8)</label><mml:math id="M8" altimg="si0008.gif" overflow="scroll"><mml:mi>j</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:mi>r</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>exp</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mo>−</mml:mo><mml:mi>r</mml:mi><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>|</mml:mo><mml:mi>θ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>k</mml:mi></mml:msubsup><mml:mrow><mml:mi>exp</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mo>−</mml:mo><mml:mi>r</mml:mi><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo>|</mml:mo><mml:mi>θ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>d</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula>for <italic>τ</italic>><italic>k</italic>. In the endemic case, we have <italic>r</italic>=0, and thus, <xref rid="eq0040" ref-type="disp-formula">(8)</xref> is simplified as<disp-formula id="eq0045"><label>(9)</label><mml:math id="M9" altimg="si0009.gif" overflow="scroll"><mml:mi>j</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:mi>r</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>|</mml:mo><mml:mi>θ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>k</mml:mi></mml:msubsup><mml:mrow><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo>|</mml:mo><mml:mi>θ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>d</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:math></disp-formula></p><p id="p0095">Let <italic>i</italic> represent a label for disease <italic>i</italic> and <italic>θ</italic><sub><italic>i</italic></sub> be the population parameter of the incubation period of disease <italic>i</italic>. The probability density of observing the illness onset at <italic>t</italic> days from immigration, <italic>g</italic><sub><italic>i</italic></sub>(<italic>t</italic>), is written as<disp-formula id="eq0050"><label>(10)</label><mml:math id="M10" altimg="si0010.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>k</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mi>d</mml:mi><mml:mi>τ</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:math></disp-formula>The function <italic>g</italic><sub><italic>i</italic></sub>(<italic>t</italic>) is the normalized version of <italic>c</italic>(<italic>t</italic>) in Eq. <xref rid="eq0035" ref-type="disp-formula">(7)</xref>. Let <italic>q</italic><sub><italic>i</italic></sub> be the prior probability of disease <italic>i</italic> in country A that may be derived from cause-specific prevalence such as those based on viral etiological study. As was discussed by <xref rid="bib7" ref-type="bibr">Nishiura et al. (2012)</xref>, a Bayesian approach is employed, and the present study uses the following formula for the differential diagnosis:<disp-formula id="eq0055"><label>(11)</label><mml:math id="M11" altimg="si0011.gif" overflow="scroll"><mml:mi>Pr</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mtext>novel</mml:mtext><mml:mspace width=".25em"></mml:mspace><mml:mtext>coronavirus</mml:mtext><mml:mo stretchy="false">|</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:munder><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:mrow><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:math></disp-formula>where <italic>i</italic>=0 denotes MERS.</p><p id="p0105">In practical instances, the exact time of illness onset may not be precisely known for all suspected cases due to coarsely recorded data, and we may only know that the illness onset occurred at time <italic>t</italic> from immigration where 0≤<italic>t</italic>≤<italic>t</italic><sub><italic>m</italic></sub>, where <italic>t</italic><sub><italic>m</italic></sub> is the possible maximum incubation period. In such an instance, we use a doubly interval censored likelihood (<xref rid="bib13" ref-type="bibr">Reich et al., 2009</xref>), i.e.,<disp-formula id="eq0060"><label>(12)</label><mml:math id="M12" altimg="si0012.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mi>Pr</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>t</mml:mi><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msubsup><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>k</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>τ</mml:mi><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mi>d</mml:mi><mml:mi>τ</mml:mi><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:math></disp-formula>which we use to compute the following crude model for prediction:<disp-formula id="eq0065"><label>(13)</label><mml:math id="M13" altimg="si0013.gif" overflow="scroll"><mml:mi>Pr</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mtext>novel</mml:mtext><mml:mspace width=".25em"></mml:mspace><mml:mtext>coronavirus</mml:mtext><mml:mo stretchy="false">|</mml:mo><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>t</mml:mi><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:munder><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:mrow><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:math></disp-formula></p><p id="p0110">It should be noted that Eq. <xref rid="eq0065" ref-type="disp-formula">(13)</xref> investigates the cumulative probability of MERS from time 0 to <italic>t</italic><sub><italic>m</italic></sub> (and thus, the interpretation is different from <xref rid="eq0055" ref-type="disp-formula">(11)</xref>), but the consistent discrete version of <xref rid="eq0055" ref-type="disp-formula">(11)</xref> can be obtained by alternatively integrating time from (<italic>t</italic><sub><italic>m</italic></sub>−1) to <italic>t</italic><sub><italic>m</italic></sub> in <xref rid="eq0060" ref-type="disp-formula">(12)</xref>.</p></sec><sec id="s0025"><label>2.3</label><title>Parameters and computational scenarios</title><p id="p0115">For illustration of the proposed predictive model, we consider the differential diagnosis between two diseases, using influenza and MERS as the case study. In addition, we consider SARS and compare it against influenza, because SARS share many clinical, virological and epidemiological features in common with MERS and the empirical data of the incubation period and epidemiological parameters were available during the early stages of MERS outbreaks (<xref rid="bib11" ref-type="bibr">Wallinga and Lipsitch, 2007</xref>, <xref rid="bib14" ref-type="bibr">Donnelly et al., 2003</xref>). Let <italic>R</italic><sub>0</sub> and <italic>T</italic><sub><italic>g</italic></sub> of influenza be 1.5 and 3.0 days, respectively. According to recent studies, <italic>R</italic><sub>0</sub> and <italic>T</italic><sub><italic>g</italic></sub> of MERS are assumed as 0.6 and 10.7 days, respectively (<xref rid="bib1" ref-type="bibr">Cauchemez et al., 2014</xref>, <xref rid="bib15" ref-type="bibr">Breban et al., 2013</xref>). Similarly, <italic>R</italic><sub>0</sub> and <italic>T</italic><sub><italic>g</italic></sub> of SARS are assumed as 3.0 and 7.0 days, respectively (<xref rid="bib14" ref-type="bibr">Donnelly et al., 2003</xref>). The incubation period was assumed to follow a lognormal distribution with the scale parameter (or the median incubation period), exp(<italic>μ</italic>)=1.6, 5.0 and 4.0 days and shape parameter <italic>σ</italic><sup>2</sup>=0.21, 0.19 and 0.37 for influenza, MERS and SARS, respectively (<xref rid="bib1" ref-type="bibr">Cauchemez et al., 2014</xref>, <xref rid="bib10" ref-type="bibr">Nishiura and Inaba, 2011</xref>, <xref rid="bib13" ref-type="bibr">Reich et al., 2009</xref>, <xref rid="bib14" ref-type="bibr">Donnelly et al., 2003</xref>). For illustration, we assumed that the length of travel was <italic>k</italic>=5 days (which is consistent with the empirical best estimate (<xref rid="bib1" ref-type="bibr">Cauchemez et al., 2014</xref>)) and also that a prior probability for each disease was 0.50. To compare against influenza, a common disease, the equal prior yields a conservative result when the diagnosis involves a novel infectious disease without known <italic>q</italic><sub><italic>i</italic></sub> (<xref rid="bib7" ref-type="bibr">Nishiura et al., 2012</xref>).</p><p id="p0120">For the exposition of our proposed method, we first compare MERS against influenza, using both continuous and discrete models (i.e. Eqs. <xref rid="eq0055" ref-type="disp-formula">(11)</xref>, <xref rid="eq0065" ref-type="disp-formula">(13)</xref>), and examine the possible time from immigration to illness onset as ranging from 0 to 10 days. As mentioned above, as an alternative to MERS during the early stages of pandemic, we also compare influenza against SARS. In both comparisons, we assume endemic and epidemic scenarios, and the latter is restricted to the early exponential growth phase. In the epidemic scenario, we use two different exponential growth rates, i.e., one assuming that the generation time is a constant, and the other assumes that the generation time follows an exponential distribution. As the sensitivity analysis, we compute the probability of influenza (in comparison with MERS) given the time from immigration to illness onset, by varying the length of travel (from 0 to 20 days), prior probability of influenza (from 0.1 to 0.9), and <italic>R</italic><sub>0</sub> of MERS (from 0.6 to 3.0) (<xref rid="bib16" ref-type="bibr">Cauchemez et al., 2013</xref>).</p></sec></sec><sec id="s0030"><label>3</label><title>Results</title><p id="p0125"><xref rid="f0010" ref-type="fig">Fig. 2</xref>A shows the probability of influenza given the exact time from immigration to illness onset (computed by Eq. <xref rid="eq0055" ref-type="disp-formula">(11)</xref>). One minus the probability of influenza gives the posterior probability of MERS. Since the median incubation of influenza is 3.4 days shorter than that of the MERS, the probability of influenza is high if the cases develop the disease shortly after immigration. However, as time goes by since immigration, the probability of influenza lowers 50% at day 2, and the probability of MERS exceeds that of influenza thereafter. Exponential growth of cases during the travel yielded higher probability of influenza than the case of uniformly distributed risk, although the difference was hardly visible on day 3 since immigration and later. If the growth rate was much greater, the probability of infection shortly before immigration would be elevated, increasing the probability of influenza. A similar qualitative pattern was seen in the comparison between influenza and SARS (<xref rid="f0010" ref-type="fig">Fig. 2</xref>B). In this comparison, the posterior probability of influenza again appeared to be greater than 50% given that a case develops illness within 2 days since immigration.<fig id="f0010"><label>Fig. 2</label><caption><p>Posterior probability of influenza in comparison with two different coronavirus infections. (A and B) The posterior probability of influenza given illness onset at <italic>t</italic> days since immigration (as compared to Middle East respiratory syndrome (MERS) and severe acute respiratory syndrome (SARS)), calculated by using Eq. <xref rid="eq0055" ref-type="disp-formula">(11)</xref>. We assumed that the travelers stay in country A for 5 days with two different rates of exponential growth (where exponential 1 corresponds to exponentially distributed generation time, while exponential 2 corresponds a constant generation time) or the uniformly distributed risk over time. The prior probability of influenza was assumed as 0.50. <italic>R</italic><sub>0</sub> of MERS was assumed to be 0.63. (C and D) The average probability of influenza given illness onset from 0 to <italic>t</italic> days since immigration (as compared to Middle East respiratory syndrome (MERS) and severe acute respiratory syndrome (SARS)), calculated by using Eq. <xref rid="eq0065" ref-type="disp-formula">(13)</xref>. Only the results that assumed exponential growth with exponentially distributed generation time are shown, but other assumption yielded quantitatively similar estimates. Other parameters are identical to those adopted in panels A and B.</p></caption><graphic xlink:href="gr2_lrg"></graphic></fig></p><p id="p0130"><xref rid="f0010" ref-type="fig">Fig. 2</xref>C and D shows the average probability of influenza, as compared with MERS and SARS, respectively, given that the case developed a disease between day 0 and day <italic>t</italic> since immigration (computed by Eq. <xref rid="eq0065" ref-type="disp-formula">(13)</xref>). Although the prediction becomes crude as compared to those based on the exact length of time in <xref rid="f0010" ref-type="fig">Fig. 2</xref>A and B, it clearly indicates that the average posterior probability of influenza is greater than 70% as long as the case develops the disease within 2 days since immigration. The probability is gradually lowered thereafter eventually reaching to 50%, i.e., the prior probability. Again, comparison between influenza and SARS yielded very similar results to that between influenza and MERS.</p><p id="p0135"><xref rid="f0015" ref-type="fig">Fig. 3</xref>A–C examines the sensitivity of the posterior probability of influenza to the duration of travel, the prior probability of influenza and <italic>R</italic><sub>0</sub> of MERS, respectively. <xref rid="f0015" ref-type="fig">Fig. 3</xref>D–F shows the corresponding results of the average probability of influenza using Eq. <xref rid="eq0065" ref-type="disp-formula">(13)</xref>. As the duration of travel was extended, it appeared that the posterior probability of influenza decreased for the early days from immigration (<xref rid="f0015" ref-type="fig">Fig. 3</xref>A and D). Since the incubation period of influenza is short (on the order of a few days at most), the long travel indirectly increased the likelihood of MERS. Short travel (e.g. 1 day) led us to have the high probability of influenza for those developing illness within 2 days since immigration, because the distribution of time from immigration to illness onset becomes closer to the incubation period distribution.<fig id="f0015"><label>Fig. 3</label><caption><p>Sensitivity of the probability of influenza to three different model variables during comparison with the Middle East respiratory syndrome (MERS). (A, B and C) Sensitivity of the posterior probability of influenza to the duration of travel, the prior probability of influenza and <italic>R</italic><sub>0</sub> of MERS, respectively (Eq. <xref rid="eq0055" ref-type="disp-formula">(11)</xref>). (D, E and F) Sensitivity of the average probability of influenza to the duration of travel, the prior probability of influenza and <italic>R</italic><sub>0</sub> of MERS, respectively (Eq. <xref rid="eq0065" ref-type="disp-formula">(13)</xref>). A & D vary the duration of travel, B & E vary the prior probability of influenza, and C & F vary the <italic>R</italic><sub>0</sub> of MERS. Unless varied in the corresponding univariate analysis, the duration of travel was 5 days, the prior probability of influenza was assumed as 0.50, and <italic>R</italic><sub>0</sub> of MERS was assumed to be 0.63. Only the results that assumed exponential growth with exponentially distributed generation time are shown, but other assumption yielded quantitatively similar estimates.</p></caption><graphic xlink:href="gr3_lrg"></graphic></fig></p><p id="p0140">The posterior probability of influenza appeared to be very sensitive to prior probability of influenza (<xref rid="f0015" ref-type="fig">Fig. 3</xref>B and E). Especially, if the prior probability of MERS was high (e.g., 90% due to widespread community transmission of MERS or if we have to examine cases at high risk such as those following close contact), the posterior probability of influenza was apparently smaller than 50% for those developing illness within 2 days since immigration. In the realistic situation with much greater endemicity of influenza than MERS for general travelers, the illness onset within 2 days from immigration was clearly suggestive of influenza. <italic>R</italic><sub>0</sub> of MERS had little impact on the prediction of influenza diagnosis (<xref rid="f0015" ref-type="fig">Fig. 3</xref>C and F), which is in line with the limited sensitivity of the posterior probability to the growth rate of infection in <xref rid="f0010" ref-type="fig">Fig. 2</xref>.</p><p id="p0145">The findings are summarized in
<xref rid="t0005" ref-type="table">Table 1</xref>. It appeared that the posterior probability of influenza for those developing illness within 2 days since immigration is strongly influenced by the prior probability of influenza. This indicates that the high probability of influenza would not be the case even for those developing illness in 2 days if MERS transmission was more widespread than influenza or if the cases were at high risk of MERS (e.g. with suspected exposure to camels or other MERS cases in hospital) (<xref rid="bib4" ref-type="bibr">Assiri et al., 2013b</xref>, <xref rid="bib18" ref-type="bibr">Reusken et al., 2013a</xref>, <xref rid="bib17" ref-type="bibr">Reusken et al., 2013b</xref>).<table-wrap position="float" id="t0005"><label>Table 1</label><caption><p>Sensitivity of differential diagnosis to four different variables.</p></caption><table frame="hsides" rules="groups"><thead><tr><th>Key variables</th><th>Baseline assumption</th><th>Sensitivity of diagnosis to the increase in assumed value</th><th>How sensitive within assumed parameter range?</th></tr></thead><tbody><tr><td>Growth rate of infection</td><td>Exponential growth or endemic steady state</td><td>(Unrealistically) large increase in the growth rate results in increase in the posterior probability of influenza</td><td>Little impact</td></tr><tr><td>Duration of travel</td><td>5 days</td><td>Longer travel yields smaller posterior probability of influenza</td><td>Moderate impact</td></tr><tr><td>Prior probability of influenza</td><td>50%</td><td>Greater prior probability of influenza yields greater posterior probability of influenza</td><td>High impact</td></tr><tr><td><italic>R</italic><sub>0</sub> of MERS (yielding the growth rate)</td><td>0.63</td><td>Greater transmissibility of MERS yields greater posterior probability of influenza</td><td>Little impact</td></tr></tbody></table></table-wrap></p></sec><sec id="s0035"><label>4</label><title>Discussion</title><p id="p0150">The present study proposed a probabilistic model that permits us to estimate the posterior probability of a specific infectious disease given the time from immigration to illness onset among imported cases. The estimation requires us to assume that we know not only the incubation period and the prior probability but also the length of travel and the transmission dynamics of exporting country. We have shown that the illness onset within 2 days from immigration is suggestive of influenza rather than MERS or SARS, which is consistent with a simpler model based on the known exact length of the incubation period (<xref rid="bib7" ref-type="bibr">Nishiura et al., 2012</xref>). The results of using SARS data were similar to those obtained using MERS data, which were consistent with similar viral etiology and common clinical characteristics between two diseases (<xref rid="bib3" ref-type="bibr">Assiri et al., 2013a</xref>, <xref rid="bib5" ref-type="bibr">, 2013</xref>, <xref rid="bib19" ref-type="bibr">Cotten et al., 2013</xref>, <xref rid="bib20" ref-type="bibr">de Wit et al., 2013</xref>). Moreover, we have demonstrated that our approach to doubly interval censored data can correspond to common practical settings in which the exact length from immigration to illness onset is not known. Assuming that the risk of MERS is likely much smaller than 0.50, the illness onset within 2 days can be said to be strongly suggestive of influenza as compared to novel coronavirus infection. Nevertheless, this predictive statement is not applicable to suspected cases at high risk of MERS-CoV infection, such as those previously exposed to camels or other confirmed cases in household or hospital (<xref rid="bib4" ref-type="bibr">Assiri et al., 2013b</xref>, <xref rid="bib18" ref-type="bibr">Reusken et al., 2013a</xref>, <xref rid="bib17" ref-type="bibr">Reusken et al., 2013b</xref>); a high weight should be given to the prior probability of MERS among these cases.</p><p id="p0155">To the best of our knowledge, the present study is the first to explicitly relate the observable time length (i.e. the time from immigration to illness onset) to the differential diagnosis of infectious diseases, examining the sensitivity of the prediction model to key model variables. By doing so, we have theoretically shown that accounting for such delay mechanism is critical not only for quantifying the natural history (<xref rid="bib10" ref-type="bibr">Nishiura and Inaba, 2011</xref>), but also for utilizing and interpreting the observable information among imported cases. Moreover, the applicability of the model is not limited to imported cases. The proposed statistical framework is widely applicable to other settings in interpreting the observable epidemiological data: the most typical application may be the distinction between nosocomial and community infections in hospitals by using the time from hospitalization to illness onset among hospitalized cases with an infectious disease (<xref rid="bib21" ref-type="bibr">Lessler et al., 2007</xref>, <xref rid="bib22" ref-type="bibr">Lessler et al., 2010</xref>, <xref rid="bib23" ref-type="bibr">Ejima et al., 2013</xref>). The formulation on this subject is our ongoing research.</p><p id="p0160">In practical terms, our proposed model not only predicts the posterior probability of influenza but also suggests that various data gaps have to be filled in empirical observation. As discussed in an earlier study (<xref rid="bib7" ref-type="bibr">Nishiura et al., 2012</xref>), it is vital to collect the information of the incubation period upon emergence of a novel infectious disease. It should also be emphasized that the viral etiological study is valuable to directly quantify <italic>q</italic><sub><italic>i</italic></sub> based on empirical data, although such data may be only applicable to general travelers (and not the travelers with close contact with other MERS cases or animals (<xref rid="bib24" ref-type="bibr">Nishiura et al., 2014</xref>)). In addition, the present study identified that addressing censored information of exposure at an exporting country requires us to understand the transmission dynamics at a global scale (and not at the country level) (<xref rid="bib25" ref-type="bibr">Lam et al., 2011</xref>). Namely, at least, either the exponential growth rate of infection, or a combination of the estimates of <italic>R</italic><sub>0</sub> and <italic>T</italic><sub><italic>g</italic></sub> has to be derived from epidemiological data (<xref rid="bib26" ref-type="bibr">Nishiura et al., 2013</xref>, <xref rid="bib27" ref-type="bibr">Nishiura, 2010</xref>). If we have a disease with similar etiology and characteristics (e.g. SARS as a substitute of MERS), <italic>R</italic><sub>0</sub>, <italic>T</italic><sub><italic>g</italic></sub> and the incubation period of the substitute disease could complement the uncertainty by the time these estimates become available for the novel disease.</p><p id="p0165">Two specific limitations have to be noted. First, our assumed exposure rests on a homogeneous population model, and the heterogeneous transmissions as well as the heterogeneous incubation period have yet to be explored extensively. Second, if the transmission dynamics is dependent on the illness onset mechanism (<xref rid="bib23" ref-type="bibr">Ejima et al., 2013</xref>, <xref rid="bib28" ref-type="bibr">Klinkenberg and Nishiura, 2011</xref>), the dependence structure has to be addressed within the model system, requiring us to account for this matter explicitly in the process of model building.</p><p id="p0170">Since the proposed clinical prediction solely relied on the incubation period and assumed transmission dynamics, improvements have to be made with a broader scope. Our ongoing future study includes an explicit assessment of the diagnostic performance of the proposed prediction system (i.e. assessment of validity and reliability), and also an inclusion of additional exposure variables other than the incubation period in the model (e.g. the presence of risky contact behavior during travel). Despite the need to drastically improve the model structure to fully achieve the practical modeling exercise, we believe that the present study successfully improved the applicability of our modeling approach to empirically observable dataset, identifying data gaps and modeling needs to be addressed in the future.</p></sec></body><back><ref-list id="bibliog0005"><title>References</title><ref id="bib3"><element-citation publication-type="journal" id="sbref1"><person-group person-group-type="author"><name><surname>Assiri</surname><given-names>A.</given-names></name><name><surname>Al-Tawfiq</surname><given-names>J.A.</given-names></name><name><surname>Al-Rabeeah</surname><given-names>A.A.</given-names></name><name><surname>Al-Rabiah</surname><given-names>F.A.</given-names></name><name><surname>Al-Hajjar</surname><given-names>S.</given-names></name><name><surname>Al-Barrak</surname><given-names>A.</given-names></name><name><surname>Flemban</surname><given-names>H.</given-names></name><name><surname>Al-Nassir</surname><given-names>W.N.</given-names></name><name><surname>Balkhy</surname><given-names>H.H.</given-names></name><name><surname>Al-Hakeem</surname><given-names>R.F.</given-names></name><name><surname>Makhdoom</surname><given-names>H.Q.</given-names></name><name><surname>Zumla</surname><given-names>A.I.</given-names></name><name><surname>Memish</surname><given-names>Z.A.</given-names></name></person-group><article-title>Epidemiological, demographic, and clinical characteristics of 47 cases of Middle East respiratory syndrome coronavirus disease from Saudi Arabia: a descriptive study</article-title><source>Lancet Infect. Dis.</source><volume>13</volume><year>2013</year><fpage>752</fpage><lpage>761</lpage><pub-id pub-id-type="pmid">23891402</pub-id></element-citation></ref><ref id="bib4"><element-citation publication-type="journal" id="sbref2"><person-group person-group-type="author"><name><surname>Assiri</surname><given-names>A.</given-names></name><name><surname>McGeer</surname><given-names>A.</given-names></name><name><surname>Perl</surname><given-names>T.M.</given-names></name><name><surname>Price</surname><given-names>C.S.</given-names></name><name><surname>Al Rabeeah</surname><given-names>A.A.</given-names></name><name><surname>Cummings</surname><given-names>D.A.</given-names></name><name><surname>Alabdullatif</surname><given-names>Z.N.</given-names></name><name><surname>Assad</surname><given-names>M.</given-names></name><name><surname>Almulhim</surname><given-names>A.</given-names></name><name><surname>Makhdoom</surname><given-names>H.</given-names></name><name><surname>Madani</surname><given-names>H.</given-names></name><name><surname>Alhakeem</surname><given-names>R.</given-names></name><name><surname>Al-Tawfiq</surname><given-names>J.A.</given-names></name><name><surname>Cotten</surname><given-names>M.</given-names></name><name><surname>Watson</surname><given-names>S.J.</given-names></name><name><surname>Kellam</surname><given-names>P.</given-names></name><name><surname>Zumla</surname><given-names>A.I.</given-names></name><name><surname>Memish</surname><given-names>Z.A.</given-names></name><name><surname>MERS-CoV</surname><given-names>K.S.A.</given-names></name></person-group><article-title>Investigation team. Hospital outbreak of Middle East respiratory syndrome coronavirus</article-title><source>N. Engl. J. Med.</source><volume>369</volume><year>2013</year><fpage>407</fpage><lpage>416</lpage><pub-id pub-id-type="pmid">23782161</pub-id></element-citation></ref><ref id="bib15"><element-citation publication-type="journal" id="sbref3"><person-group person-group-type="author"><name><surname>Breban</surname><given-names>R.</given-names></name><name><surname>Riou</surname><given-names>J.</given-names></name><name><surname>Fontanet</surname><given-names>A.</given-names></name></person-group><article-title>Interhuman transmissibility of Middle East respiratory syndrome coronavirus: estimation of pandemic risk</article-title><source>Lancet</source><volume>382</volume><year>2013</year><fpage>694</fpage><lpage>699</lpage><pub-id pub-id-type="pmid">23831141</pub-id></element-citation></ref><ref id="bib16"><element-citation publication-type="journal" id="sbref4"><person-group person-group-type="author"><name><surname>Cauchemez</surname><given-names>S.</given-names></name><name><surname>Van Kerkhove</surname><given-names>M.D.</given-names></name><name><surname>Riley</surname><given-names>S.</given-names></name><name><surname>Donnelly</surname><given-names>C.A.</given-names></name><name><surname>Fraser</surname><given-names>C.</given-names></name><name><surname>Ferguson</surname><given-names>N.M.</given-names></name></person-group><article-title>Transmission scenarios for Middle East Respiratory Syndrome Coronavirus (MERS-CoV) and how to tell them apart</article-title><source>Eurosurveillance</source><volume>18</volume><year>2013</year><comment>(pii=20503)</comment></element-citation></ref><ref id="bib1"><element-citation publication-type="journal" id="sbref5"><person-group person-group-type="author"><name><surname>Cauchemez</surname><given-names>S.</given-names></name><name><surname>Fraser</surname><given-names>C.</given-names></name><name><surname>Van Kerkhove</surname><given-names>M.D.</given-names></name><name><surname>Donnelly</surname><given-names>C.A.</given-names></name><name><surname>Riley</surname><given-names>S.</given-names></name><name><surname>Rambaut</surname><given-names>A.</given-names></name><name><surname>Enouf</surname><given-names>V.</given-names></name><name><surname>van der Werf</surname><given-names>S.</given-names></name><name><surname>Ferguson</surname><given-names>N.M.</given-names></name></person-group><article-title>Middle East respiratory syndrome coronavirus: quantification of the extent of the epidemic, surveillance biases, and transmissibility</article-title><source>Lancet Infect. Dis.</source><volume>14</volume><year>2014</year><fpage>50</fpage><lpage>56</lpage><pub-id pub-id-type="pmid">24239323</pub-id></element-citation></ref><ref id="bib9"><element-citation publication-type="journal" id="sbref6"><person-group person-group-type="author"><name><surname>Clancy</surname><given-names>D.</given-names></name><name><surname>O’Neill</surname><given-names>P.D.</given-names></name></person-group><article-title>Bayesian estimation of the basic reproduction number in stochastic epidemic models</article-title><source>Bayesian Anal.</source><volume>3</volume><year>2008</year><fpage>737</fpage><lpage>758</lpage></element-citation></ref><ref id="bib19"><element-citation publication-type="journal" id="sbref7"><person-group person-group-type="author"><name><surname>Cotten</surname><given-names>M.</given-names></name><name><surname>Watson</surname><given-names>S.J.</given-names></name><name><surname>Kellam</surname><given-names>P.</given-names></name><name><surname>Al-Rabeeah</surname><given-names>A.A.</given-names></name><name><surname>Makhdoom</surname><given-names>H.Q.</given-names></name><name><surname>Assiri</surname><given-names>A.</given-names></name><name><surname>Al-Tawfiq</surname><given-names>J.A.</given-names></name><name><surname>Alhakeem</surname><given-names>R.F.</given-names></name><name><surname>Madani</surname><given-names>H.</given-names></name><name><surname>AlRabiah</surname><given-names>F.A.</given-names></name><name><surname>Al Hajjar</surname><given-names>S.</given-names></name><name><surname>Al-nassir</surname><given-names>W.N.</given-names></name><name><surname>Albarrak</surname><given-names>A.</given-names></name><name><surname>Flemban</surname><given-names>H.</given-names></name><name><surname>Balkhy</surname><given-names>H.H.</given-names></name><name><surname>Alsubaie</surname><given-names>S.</given-names></name><name><surname>Palser</surname><given-names>A.L.</given-names></name><name><surname>Gall</surname><given-names>A.</given-names></name><name><surname>Bashford-Rogers</surname><given-names>R.</given-names></name><name><surname>Rambaut</surname><given-names>A.</given-names></name><name><surname>Zumla</surname><given-names>A.I.</given-names></name><name><surname>Memish</surname><given-names>Z.A.</given-names></name></person-group><article-title>Transmission and evolution of the Middle East respiratory syndrome coronavirus in Saudi Arabia: a descriptive genomic study</article-title><source>Lancet</source><volume>382</volume><year>2013</year><fpage>1993</fpage><lpage>2002</lpage><pub-id pub-id-type="pmid">24055451</pub-id></element-citation></ref><ref id="bib20"><element-citation publication-type="journal" id="sbref8"><person-group person-group-type="author"><name><surname>de Wit</surname><given-names>E.</given-names></name><name><surname>Rasmussen</surname><given-names>A.L.</given-names></name><name><surname>Falzarano</surname><given-names>D.</given-names></name><name><surname>Bushmaker</surname><given-names>T.</given-names></name><name><surname>Feldmann</surname><given-names>F.</given-names></name><name><surname>Brining</surname><given-names>D.L.</given-names></name><name><surname>Fischer</surname><given-names>E.R.</given-names></name><name><surname>Martellaro</surname><given-names>C.</given-names></name><name><surname>Okumura</surname><given-names>A.</given-names></name><name><surname>Chang</surname><given-names>J.</given-names></name><name><surname>Scott</surname><given-names>D.</given-names></name><name><surname>Benecke</surname><given-names>A.G.</given-names></name><name><surname>Katze</surname><given-names>M.G.</given-names></name><name><surname>Feldmann</surname><given-names>H.</given-names></name><name><surname>Munster</surname><given-names>V.J.</given-names></name></person-group><article-title>Middle East respiratory syndrome coronavirus (MERS-CoV) causes transient lower respiratory tract infection in rhesus macaques</article-title><source>Proc. Natl. Acad. Sci. USA</source><volume>110</volume><year>2013</year><fpage>16598</fpage><lpage>16603</lpage><pub-id pub-id-type="pmid">24062443</pub-id></element-citation></ref><ref id="bib14"><element-citation publication-type="journal" id="sbref9"><person-group person-group-type="author"><name><surname>Donnelly</surname><given-names>C.A.</given-names></name><name><surname>Ghani</surname><given-names>A.C.</given-names></name><name><surname>Leung</surname><given-names>G.M.</given-names></name><name><surname>Hedley</surname><given-names>A.J.</given-names></name><name><surname>Fraser</surname><given-names>C.</given-names></name><name><surname>Riley</surname><given-names>S.</given-names></name><name><surname>Abu-Raddad</surname><given-names>L.J.</given-names></name><name><surname>Ho</surname><given-names>L.M.</given-names></name><name><surname>Thach</surname><given-names>T.Q.</given-names></name><name><surname>Chau</surname><given-names>P.</given-names></name><name><surname>Chan</surname><given-names>K.P.</given-names></name><name><surname>Lam</surname><given-names>T.H.</given-names></name><name><surname>Tse</surname><given-names>L.Y.</given-names></name><name><surname>Tsang</surname><given-names>T.</given-names></name><name><surname>Liu</surname><given-names>S.H.</given-names></name><name><surname>Kong</surname><given-names>J.H.</given-names></name><name><surname>Lau</surname><given-names>E.M.</given-names></name><name><surname>Ferguson</surname><given-names>N.M.</given-names></name><name><surname>Anderson</surname><given-names>R.M.</given-names></name></person-group><article-title>Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong</article-title><source>Lancet</source><volume>361</volume><year>2003</year><fpage>1761</fpage><lpage>1766</lpage><comment>(referred to Erratum in Lancet 2003; 361:1832)</comment><pub-id pub-id-type="pmid">12781533</pub-id></element-citation></ref><ref id="bib23"><element-citation publication-type="journal" id="sbref10"><person-group person-group-type="author"><name><surname>Ejima</surname><given-names>K.</given-names></name><name><surname>Aihara</surname><given-names>K.</given-names></name><name><surname>Nishiura</surname><given-names>H.</given-names></name></person-group><article-title>The impact of model building on the transmission dynamics under vaccination: observable (symptom-based) versus unobservable (contagiousness-dependent) approaches</article-title><source>PLoS One</source><volume>8</volume><year>2013</year><fpage>e62062</fpage><pub-id pub-id-type="pmid">23593507</pub-id></element-citation></ref><ref id="bib2"><element-citation publication-type="journal" id="sbref11"><person-group person-group-type="author"><name><surname>Fisman</surname><given-names>D.N.</given-names></name><name><surname>Tuite</surname><given-names>A.R.</given-names></name></person-group><article-title>The epidemiology of MERS-CoV</article-title><source>Lancet Infect. Dis.</source><volume>14</volume><year>2014</year><fpage>6</fpage><lpage>7</lpage><pub-id pub-id-type="pmid">24239325</pub-id></element-citation></ref><ref id="bib5"><element-citation publication-type="journal" id="sbref12"><person-group person-group-type="author"><name><surname>Guery</surname><given-names>B.</given-names></name><name><surname>Poissy</surname><given-names>J.</given-names></name><name><surname>el Mansouf</surname><given-names>L.</given-names></name><name><surname>Séjourné</surname><given-names>C.</given-names></name><name><surname>Ettahar</surname><given-names>N.</given-names></name><name><surname>Lemaire</surname><given-names>X.</given-names></name><name><surname>Vuotto</surname><given-names>F.</given-names></name><name><surname>Goffard</surname><given-names>A.</given-names></name><name><surname>Behillil</surname><given-names>S.</given-names></name><name><surname>Enouf</surname><given-names>V.</given-names></name><name><surname>Caro</surname><given-names>V.</given-names></name><name><surname>Mailles</surname><given-names>A.</given-names></name><name><surname>Che</surname><given-names>D.</given-names></name><name><surname>Manuguerra</surname><given-names>J.C.</given-names></name><name><surname>Mathieu</surname><given-names>D.</given-names></name><name><surname>Fontanet</surname><given-names>A.</given-names></name><name><surname>van der Werf</surname><given-names>S.</given-names></name><collab>MERS-CoV study group</collab></person-group><article-title>Clinical features and viral diagnosis of two cases of infection with Middle East Respiratory Syndrome coronavirus: a report of nosocomial transmission</article-title><source>Lancet</source><volume>381</volume><year>2013</year><fpage>2265</fpage><lpage>2272</lpage><pub-id pub-id-type="pmid">23727167</pub-id></element-citation></ref><ref id="bib28"><element-citation publication-type="journal" id="sbref13"><person-group person-group-type="author"><name><surname>Klinkenberg</surname><given-names>D.</given-names></name><name><surname>Nishiura</surname><given-names>H.</given-names></name></person-group><article-title>The correlation between infectivity and incubation period of measles, estimated from households with two cases</article-title><source>J. Theor. Biol.</source><volume>284</volume><issue>1</issue><year>2011</year><fpage>52</fpage><lpage>60</lpage><pub-id pub-id-type="pmid">21704640</pub-id></element-citation></ref><ref id="bib25"><element-citation publication-type="journal" id="sbref14"><person-group person-group-type="author"><name><surname>Lam</surname><given-names>E.H.</given-names></name><name><surname>Cowling</surname><given-names>B.J.</given-names></name><name><surname>Cook</surname><given-names>A.R.</given-names></name><name><surname>Wong</surname><given-names>J.Y.</given-names></name><name><surname>Lau</surname><given-names>M.S.</given-names></name><name><surname>Nishiura</surname><given-names>H.</given-names></name></person-group><article-title>The feasibility of age-specific travel restrictions during influenza pandemics</article-title><source>Theor. Biol. Med. Model.</source><volume>8</volume><year>2011</year><fpage>44</fpage><pub-id pub-id-type="pmid">22078655</pub-id></element-citation></ref><ref id="bib21"><element-citation publication-type="journal" id="sbref15"><person-group person-group-type="author"><name><surname>Lessler</surname><given-names>J.</given-names></name><name><surname>Brookmeyer</surname><given-names>R.</given-names></name><name><surname>Perl</surname><given-names>T.M.</given-names></name></person-group><article-title>An evaluation of classification rules based on date of symptom onset to identify health-care associated infections</article-title><source>Am. J. Epidemiol.</source><volume>166</volume><year>2007</year><fpage>1220</fpage><lpage>1229</lpage><pub-id pub-id-type="pmid">17702972</pub-id></element-citation></ref><ref id="bib22"><element-citation publication-type="journal" id="sbref16"><person-group person-group-type="author"><name><surname>Lessler</surname><given-names>J.</given-names></name><name><surname>Brookmeyer</surname><given-names>R.</given-names></name><name><surname>Reich</surname><given-names>N.G.</given-names></name><name><surname>Nelson</surname><given-names>K.E.</given-names></name><name><surname>Cummings</surname><given-names>D.A.</given-names></name><name><surname>Perl</surname><given-names>T.M.</given-names></name></person-group><article-title>Identifying the probable timing and setting of respiratory virus infections</article-title><source>Infect. Control Hosp. Epidemiol.</source><volume>31</volume><year>2010</year><fpage>809</fpage><lpage>815</lpage><pub-id pub-id-type="pmid">20569117</pub-id></element-citation></ref><ref id="bib27"><element-citation publication-type="journal" id="sbref17"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H.</given-names></name></person-group><article-title>Time variations in the generation time of an infectious disease: implications for sampling to appropriately quantify transmission potential</article-title><source>Math. Biosci. Eng.</source><volume>7</volume><year>2010</year><fpage>851</fpage><lpage>869</lpage><pub-id pub-id-type="pmid">21077712</pub-id></element-citation></ref><ref id="bib10"><element-citation publication-type="journal" id="sbref18"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H.</given-names></name><name><surname>Inaba</surname><given-names>H.</given-names></name></person-group><article-title>Estimation of the incubation period of influenza A (H1N1-2009) among imported cases: addressing censoring using outbreak data at the origin of importation</article-title><source>J. Theor. Biol.</source><volume>272</volume><year>2011</year><fpage>123</fpage><lpage>130</lpage><pub-id pub-id-type="pmid">21168422</pub-id></element-citation></ref><ref id="bib8"><element-citation publication-type="journal" id="sbref19"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H.</given-names></name><name><surname>Kamiya</surname><given-names>K.</given-names></name></person-group><article-title>Fever screening during the influenza (H1N1-2009) pandemic at Narita International Airport, Japan</article-title><source>BMC Infect. Dis.</source><volume>11</volume><year>2011</year><fpage>111</fpage><pub-id pub-id-type="pmid">21539735</pub-id></element-citation></ref><ref id="bib7"><element-citation publication-type="journal" id="sbref20"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H.</given-names></name><name><surname>Mizumoto</surname><given-names>K.</given-names></name><name><surname>Ejima</surname><given-names>K.</given-names></name><name><surname>Zhong</surname><given-names>Y.</given-names></name><name><surname>Cowling</surname><given-names>B.</given-names></name><name><surname>Omori</surname><given-names>R.</given-names></name></person-group><article-title>Incubation period as part of the case definition of severe respiratory illness caused by a novel coronavirus</article-title><source>Eurosurveillance</source><volume>17</volume><year>2012</year><comment>(pii=20296)</comment></element-citation></ref><ref id="bib26"><element-citation publication-type="journal" id="sbref21"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H.</given-names></name><name><surname>Mizumoto</surname><given-names>K.</given-names></name><name><surname>Ejima</surname><given-names>K.</given-names></name></person-group><article-title>How to interpret the transmissibility of novel influenza A(H7N9): an analysis of initial epidemiological data of human cases from China</article-title><source>Theor. Biol. Med. Model.</source><volume>10</volume><year>2013</year><fpage>30</fpage><pub-id pub-id-type="pmid">23642092</pub-id></element-citation></ref><ref id="bib24"><element-citation publication-type="journal" id="sbref22"><person-group person-group-type="author"><name><surname>Nishiura</surname><given-names>H.</given-names></name><name><surname>Ejima</surname><given-names>K.</given-names></name><name><surname>Mizumoto</surname><given-names>K.</given-names></name></person-group><article-title>Missing information in animal surveillance of MERS-CoV</article-title><source>Lancet Infect. Dis.</source><volume>14</volume><issue>2</issue><year>2014</year><comment>(in press)</comment></element-citation></ref><ref id="bib13"><element-citation publication-type="journal" id="sbref23"><person-group person-group-type="author"><name><surname>Reich</surname><given-names>N.G.</given-names></name><name><surname>Lessler</surname><given-names>J.</given-names></name><name><surname>Cummings</surname><given-names>D.A.</given-names></name><name><surname>Brookmeyer</surname><given-names>R.</given-names></name></person-group><article-title>Estimating incubation period distributions with coarse data</article-title><source>Stat. Med.</source><volume>28</volume><issue>22</issue><year>2009</year><fpage>2769</fpage><lpage>2784</lpage><pub-id pub-id-type="pmid">19598148</pub-id></element-citation></ref><ref id="bib18"><element-citation publication-type="journal" id="sbref24"><person-group person-group-type="author"><name><surname>Reusken</surname><given-names>C.</given-names></name><name><surname>Ababneh</surname><given-names>M.</given-names></name><name><surname>Raj</surname><given-names>V.</given-names></name><name><surname>Meyer</surname><given-names>B.</given-names></name><name><surname>Eljarah</surname><given-names>A.</given-names></name><name><surname>Abutarbush</surname><given-names>S.</given-names></name><name><surname>Godeke</surname><given-names>G.</given-names></name><name><surname>Bestebroer</surname><given-names>T.</given-names></name><name><surname>Zutt</surname><given-names>I.</given-names></name><name><surname>Muller</surname><given-names>M.</given-names></name><name><surname>Bosch</surname><given-names>B.</given-names></name><name><surname>Rottier</surname><given-names>P.</given-names></name><name><surname>Osterhaus</surname><given-names>A.</given-names></name><name><surname>Drosten</surname><given-names>C.</given-names></name><name><surname>Haagmans</surname><given-names>B.</given-names></name><name><surname>Koopmans</surname><given-names>M.</given-names></name></person-group><article-title>Middle East Respiratory Syndrome coronavirus (MERS-CoV) serology in major livestock species in an affected region in Jordan, June to September 2013</article-title><source>Eurosurveillance</source><volume>18</volume><year>2013</year><comment>(pii=20662)</comment></element-citation></ref><ref id="bib17"><element-citation publication-type="journal" id="sbref25"><person-group person-group-type="author"><name><surname>Reusken</surname><given-names>C.B.</given-names></name><name><surname>Haagmans</surname><given-names>B.L.</given-names></name><name><surname>Müller</surname><given-names>M.A.</given-names></name><name><surname>Gutierrez</surname><given-names>C.</given-names></name><name><surname>Godeke</surname><given-names>G.J.</given-names></name><name><surname>Meyer</surname><given-names>B.</given-names></name><name><surname>Muth</surname><given-names>D.</given-names></name><name><surname>Raj</surname><given-names>V.S.</given-names></name><name><surname>Smits-De Vries</surname><given-names>L.</given-names></name><name><surname>Corman</surname><given-names>V.M.</given-names></name><name><surname>Drexler</surname><given-names>J.F.</given-names></name><name><surname>Smits</surname><given-names>S.L.</given-names></name><name><surname>El Tahir</surname><given-names>Y.E.</given-names></name><name><surname>De Sousa</surname><given-names>R.</given-names></name><name><surname>van Beek</surname><given-names>J.</given-names></name><name><surname>Nowotny</surname><given-names>N.</given-names></name><name><surname>van Maanen</surname><given-names>K.</given-names></name><name><surname>Hidalgo-Hermoso</surname><given-names>E.</given-names></name><name><surname>Bosch</surname><given-names>B.J.</given-names></name><name><surname>Rottier</surname><given-names>P.</given-names></name><name><surname>Osterhaus</surname><given-names>A.</given-names></name><name><surname>Gortázar-Schmidt</surname><given-names>C.</given-names></name><name><surname>Drosten</surname><given-names>C.</given-names></name><name><surname>Koopmans</surname><given-names>M.P.</given-names></name></person-group><article-title>Middle East respiratory syndrome coronavirus neutralising serum antibodies in dromedary camels: a comparative serological study</article-title><source>Lancet Infect. Dis.</source><volume>13</volume><year>2013</year><fpage>859</fpage><lpage>866</lpage><pub-id pub-id-type="pmid">23933067</pub-id></element-citation></ref><ref id="bib12"><element-citation publication-type="journal" id="sbref26"><person-group person-group-type="author"><name><surname>Roberts</surname><given-names>M.G.</given-names></name><name><surname>Heesterbeek</surname><given-names>J.A.</given-names></name></person-group><article-title>Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection</article-title><source>J. Math. Biol.</source><volume>55</volume><year>2007</year><fpage>803</fpage><lpage>816</lpage><pub-id pub-id-type="pmid">17684743</pub-id></element-citation></ref><ref id="bib6"><mixed-citation publication-type="other" id="othref0005">Saudi boy in Hong Kong has Flu, not Sars-like Virus: South China Morning Post, 8 October, 2012. Available from: <ext-link ext-link-type="uri" xlink:href="http://www.scmp.com/news/hong-kong/article/1056321/saudi-boy-tests-negative-sars-virus-hong-kong-health-officials-say" id="ir0005">〈http://www.scmp.com/news/hong-kong/article/1056321/saudi-boy-tests-negative-sars-virus-hong-kong-health-officials-say〉</ext-link> (accessed 18.12.12).</mixed-citation></ref><ref id="bib11"><element-citation publication-type="journal" id="sbref27"><person-group person-group-type="author"><name><surname>Wallinga</surname><given-names>J.</given-names></name><name><surname>Lipsitch</surname><given-names>M.</given-names></name></person-group><article-title>How generation intervals shape the relationship between growth rates and reproductive numbers</article-title><source>Proc. R. Soc. Lond. Ser. B</source><volume>274</volume><year>2007</year><fpage>599</fpage><lpage>604</lpage></element-citation></ref></ref-list><ack id="ack0005"><title>Acknowledgment</title><p>HN received funding support from <funding-source id="GS1">Takahashi Industrial and Economic Research Foundation</funding-source> and the <funding-source id="GS2">Japan Science and Technology Agency (JST) PRESTO program</funding-source>. KE received scholarship support from the <funding-source id="GS3">Japan Society for Promotion of Science (JSPS)</funding-source>. KA received funding support from the Aihara Project, the FIRST program from <funding-source id="GS4">JSPS</funding-source>, initiated by CSTP. The funding bodies were not involved in the collection, analysis and interpretation of data, the writing of the manuscript or the decision to submit for publication.</p></ack></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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