Links to Exploration step
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Modelling the spreading rate of controlled communicable epidemics through an entropy-based thermodynamic model</title><author><name sortKey="Wang, Wenbin" sort="Wang, Wenbin" uniqKey="Wang W" first="Wenbin" last="Wang">Wenbin Wang</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author><author><name sortKey="Wu, Ziniu" sort="Wu, Ziniu" uniqKey="Wu Z" first="Ziniu" last="Wu">Ziniu Wu</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author><author><name sortKey="Wang, Chunfeng" sort="Wang, Chunfeng" uniqKey="Wang C" first="Chunfeng" last="Wang">Chunfeng Wang</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author><author><name sortKey="Hu, Ruifeng" sort="Hu, Ruifeng" uniqKey="Hu R" first="Ruifeng" last="Hu">Ruifeng Hu</name><affiliation><nlm:aff id="Aff2"><institution-wrap><institution-id institution-id-type="GRID">grid.440736.2</institution-id><institution-id institution-id-type="ISNI">0000 0001 0707 115X</institution-id><institution>School of Electro-Mechanical Engineering,</institution><institution>Xidian University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmc">7111546</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7111546</idno><idno type="RBID">PMC:7111546</idno><idno type="doi">10.1007/s11433-013-5321-0</idno><idno type="pmid">NONE</idno><date when="2013">2013</date><idno type="wicri:Area/Pmc/Corpus">000466</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000466</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Modelling the spreading rate of controlled communicable epidemics through an entropy-based thermodynamic model</title><author><name sortKey="Wang, Wenbin" sort="Wang, Wenbin" uniqKey="Wang W" first="Wenbin" last="Wang">Wenbin Wang</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author><author><name sortKey="Wu, Ziniu" sort="Wu, Ziniu" uniqKey="Wu Z" first="Ziniu" last="Wu">Ziniu Wu</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author><author><name sortKey="Wang, Chunfeng" sort="Wang, Chunfeng" uniqKey="Wang C" first="Chunfeng" last="Wang">Chunfeng Wang</name><affiliation><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author><author><name sortKey="Hu, Ruifeng" sort="Hu, Ruifeng" uniqKey="Hu R" first="Ruifeng" last="Hu">Ruifeng Hu</name><affiliation><nlm:aff id="Aff2"><institution-wrap><institution-id institution-id-type="GRID">grid.440736.2</institution-id><institution-id institution-id-type="ISNI">0000 0001 0707 115X</institution-id><institution>School of Electro-Mechanical Engineering,</institution><institution>Xidian University,</institution></institution-wrap>Beijing, 100084 China</nlm:aff></affiliation></author></analytic><series><title level="j">Science China. Physics, Mechanics & Astronomy</title><idno type="ISSN">1674-7348</idno><idno type="eISSN">1869-1927</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics assumed to be governed by controlling efforts of multiple scales so that an entropy is associated with the system. All the epidemic details are factored into a single and time-dependent coefficient, the functional form of this coefficient is found through four constraints, including notably the existence of an inflexion point and a maximum. The model is solved to give a log-normal distribution for the spread rate, for which a Shannon entropy can be defined. The only parameter, that characterizes the width of the distribution function, is uniquely determined through maximizing the rate of entropy production. This entropy-based thermodynamic (EBT) model predicts the number of hospitalized cases with a reasonable accuracy for SARS in the year 2003. This EBT model can be of use for potential epidemics such as avian influenza and H7N9 in China.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Ma, Z" uniqKey="Ma Z">Z Ma</name></author><author><name sortKey="Zhou, Y" uniqKey="Zhou Y">Y Zhou</name></author><author><name sortKey="Wu, J" uniqKey="Wu J">J Wu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bauch, C T" uniqKey="Bauch C">C T Bauch</name></author><author><name sortKey="Lloyd Smith, J O" uniqKey="Lloyd Smith J">J O Lloyd-Smith</name></author><author><name sortKey="Coffee, M P" uniqKey="Coffee M">M P Coffee</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bian, L" uniqKey="Bian L">L Bian</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></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Riley, S" uniqKey="Riley S">S Riley</name></author><author><name sortKey="Fraster, C" uniqKey="Fraster C">C Fraster</name></author><author><name sortKey="Donnelly, C A" uniqKey="Donnelly C">C A Donnelly</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lipsitch, M" uniqKey="Lipsitch M">M Lipsitch</name></author><author><name sortKey="Cohen, T" uniqKey="Cohen T">T Cohen</name></author><author><name sortKey="Cooper, B" uniqKey="Cooper B">B Cooper</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dye, C" uniqKey="Dye C">C Dye</name></author><author><name sortKey="Gay, N" uniqKey="Gay N">N Gay</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Jia, N" uniqKey="Jia N">N Jia</name></author><author><name sortKey="Tsui, L" uniqKey="Tsui L">L Tsui</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Watts, D J" uniqKey="Watts D">D J Watts</name></author><author><name sortKey="Muhamad, R" uniqKey="Muhamad R">R Muhamad</name></author><author><name sortKey="Medina, D C" uniqKey="Medina D">D C Medina</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhang, Z B" uniqKey="Zhang Z">Z B Zhang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kenah, E" uniqKey="Kenah E">E Kenah</name></author><author><name sortKey="Robins, J M" uniqKey="Robins J">J M Robins</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bian, L" uniqKey="Bian L">L Bian</name></author><author><name sortKey="Liebner, D" uniqKey="Liebner D">D Liebner</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Yu, X L" uniqKey="Yu X">X L Yu</name></author><author><name sortKey="Wang, X Y" uniqKey="Wang X">X Y Wang</name></author><author><name sortKey="Zhang, D M" uniqKey="Zhang D">D M Zhang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dybiec, B" uniqKey="Dybiec B">B Dybiec</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Dybiec, B" uniqKey="Dybiec B">B Dybiec</name></author><author><name sortKey="Kleczkowski, A" uniqKey="Kleczkowski A">A Kleczkowski</name></author><author><name sortKey="Gilligan, C A" uniqKey="Gilligan C">C A Gilligan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Anderson, R M" uniqKey="Anderson R">R M Anderson</name></author><author><name sortKey="May, R M" uniqKey="May R">R M May</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mollison, D" uniqKey="Mollison D">D Mollison</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Edelstein Keshet, L" uniqKey="Edelstein Keshet L">L Edelstein-Keshet</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wu, Z N" uniqKey="Wu Z">Z N Wu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Brauer, F" uniqKey="Brauer F">F Brauer</name></author><author><name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C Castillo-Chavez</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ahmed, E" uniqKey="Ahmed E">E Ahmed</name></author><author><name sortKey="Agiza, H N" uniqKey="Agiza H">H N Agiza</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Greenhalgh, D" uniqKey="Greenhalgh D">D Greenhalgh</name></author><author><name sortKey="Das, P" uniqKey="Das P">P Das</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Weber, A" uniqKey="Weber A">A Weber</name></author><author><name sortKey="Weber, M" uniqKey="Weber M">M Weber</name></author><author><name sortKey="Milligan, P" uniqKey="Milligan P">P Milligan</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pybus, O G" uniqKey="Pybus O">O G Pybus</name></author><author><name sortKey="Charleston, M A" uniqKey="Charleston M">M A Charleston</name></author><author><name sortKey="Gupta, S" uniqKey="Gupta S">S Gupta</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Anderson, J D" uniqKey="Anderson J">J D Anderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ziegler, H" uniqKey="Ziegler H">H Ziegler</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Gao, R B" uniqKey="Gao R">R B Gao</name></author><author><name sortKey="Cao, B" uniqKey="Cao B">B Cao</name></author><author><name sortKey="Hu, Y W" uniqKey="Hu Y">Y W Hu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wen, Y M" uniqKey="Wen Y">Y M Wen</name></author><author><name sortKey="Klenk, H D" uniqKey="Klenk H">H D Klenk</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="She, Z S" uniqKey="She Z">Z S She</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">Sci China Phys Mech Astron</journal-id><journal-id journal-id-type="iso-abbrev">Sci China Phys Mech Astron</journal-id><journal-title-group><journal-title>Science China. Physics, Mechanics & Astronomy</journal-title></journal-title-group><issn pub-type="ppub">1674-7348</issn><issn pub-type="epub">1869-1927</issn><publisher><publisher-name>Springer Berlin Heidelberg</publisher-name><publisher-loc>Berlin/Heidelberg</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmc">7111546</article-id><article-id pub-id-type="publisher-id">5321</article-id><article-id pub-id-type="doi">10.1007/s11433-013-5321-0</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Modelling the spreading rate of controlled communicable epidemics through an entropy-based thermodynamic model</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Wang</surname><given-names>WenBin</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Wu</surname><given-names>ZiNiu</given-names></name><address><email>ziniuwu@tsinghua.edu.cn</email></address><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Wang</surname><given-names>ChunFeng</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Hu</surname><given-names>RuiFeng</given-names></name><xref ref-type="aff" rid="Aff2">2</xref></contrib><aff id="Aff1"><label>1</label><institution-wrap><institution-id institution-id-type="GRID">grid.12527.33</institution-id><institution-id institution-id-type="ISNI">0000000106623178</institution-id><institution>Department of Engineering Mechanics,</institution><institution>Tsinghua University,</institution></institution-wrap>Beijing, 100084 China</aff><aff id="Aff2"><label>2</label><institution-wrap><institution-id institution-id-type="GRID">grid.440736.2</institution-id><institution-id institution-id-type="ISNI">0000 0001 0707 115X</institution-id><institution>School of Electro-Mechanical Engineering,</institution><institution>Xidian University,</institution></institution-wrap>Beijing, 100084 China</aff></contrib-group><pub-date pub-type="epub"><day>3</day><month>10</month><year>2013</year></pub-date><pub-date pub-type="ppub"><year>2013</year></pub-date><volume>56</volume><issue>11</issue><fpage>2143</fpage><lpage>2150</lpage><history><date date-type="received"><day>23</day><month>4</month><year>2013</year></date><date date-type="accepted"><day>29</day><month>7</month><year>2013</year></date></history><permissions><copyright-statement>© Science China Press and Springer-Verlag Berlin Heidelberg 2013</copyright-statement><license><license-p>This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.</license-p></license></permissions><abstract id="Abs1"><p>A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics assumed to be governed by controlling efforts of multiple scales so that an entropy is associated with the system. All the epidemic details are factored into a single and time-dependent coefficient, the functional form of this coefficient is found through four constraints, including notably the existence of an inflexion point and a maximum. The model is solved to give a log-normal distribution for the spread rate, for which a Shannon entropy can be defined. The only parameter, that characterizes the width of the distribution function, is uniquely determined through maximizing the rate of entropy production. This entropy-based thermodynamic (EBT) model predicts the number of hospitalized cases with a reasonable accuracy for SARS in the year 2003. This EBT model can be of use for potential epidemics such as avian influenza and H7N9 in China.</p></abstract><kwd-group xml:lang="en"><title>Keywords</title><kwd>epidemics</kwd><kwd>entropy</kwd><kwd>inflexion point</kwd></kwd-group><custom-meta-group><custom-meta><meta-name>issue-copyright-statement</meta-name><meta-value>© Science China Press and Springer-Verlag Berlin Heidelberg 2013</meta-value></custom-meta></custom-meta-group></article-meta></front><back><fn-group><fn><p>Recommended by SHE ZhenSu (Associate Editor)</p></fn></fn-group><ref-list id="Bib1"><title>References</title><ref id="CR1"><label>1</label><element-citation publication-type="book"><person-group person-group-type="author"><collab>Kamps-Hoffmann.</collab></person-group><source>SARS References-05/2003[OL]</source><year>2003</year><publisher-loc>Paris</publisher-loc><publisher-name>Flying Publishers</publisher-name></element-citation></ref><ref id="CR2"><label>2</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Ma</surname><given-names>Z</given-names></name><name><surname>Zhou</surname><given-names>Y</given-names></name><name><surname>Wu</surname><given-names>J</given-names></name></person-group><source>Modeling and Dynamics of Infectious Diseases</source><year>2009</year><publisher-loc>Singapore</publisher-loc><publisher-name>World Scientific Publishing</publisher-name></element-citation></ref><ref id="CR3"><label>3</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bauch</surname><given-names>C T</given-names></name><name><surname>Lloyd-Smith</surname><given-names>J O</given-names></name><name><surname>Coffee</surname><given-names>M P</given-names></name><etal></etal></person-group><article-title>Dynamically modeling SARS and other newly emerging respiratory illnesses: past, present, and future</article-title><source>Epidemiology</source><year>2005</year><volume>16</volume><fpage>791</fpage><lpage>801</lpage><pub-id pub-id-type="doi">10.1097/01.ede.0000181633.80269.4c</pub-id><pub-id pub-id-type="pmid">16222170</pub-id></element-citation></ref><ref id="CR4"><label>4</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bian</surname><given-names>L</given-names></name></person-group><article-title>Spatial approaches to modeling dispersion of communicable diseases — A review</article-title><source>Trans GIS</source><year>2012</year><volume>17</volume><fpage>1</fpage><lpage>17</lpage><pub-id pub-id-type="doi">10.1111/j.1467-9671.2012.01329.x</pub-id></element-citation></ref><ref id="CR5"><label>5</label><element-citation publication-type="journal"><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><etal></etal></person-group><article-title>Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong</article-title><source>The Lancet</source><year>2003</year><volume>361</volume><fpage>1761</fpage><lpage>1766</lpage><pub-id pub-id-type="doi">10.1016/S0140-6736(03)13410-1</pub-id></element-citation></ref><ref id="CR6"><label>6</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Riley</surname><given-names>S</given-names></name><name><surname>Fraster</surname><given-names>C</given-names></name><name><surname>Donnelly</surname><given-names>C A</given-names></name><etal></etal></person-group><article-title>Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions</article-title><source>Science</source><year>2003</year><volume>300</volume><fpage>1961</fpage><lpage>1966</lpage><pub-id pub-id-type="doi">10.1126/science.1086478</pub-id><pub-id pub-id-type="pmid">12766206</pub-id></element-citation></ref><ref id="CR7"><label>7</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lipsitch</surname><given-names>M</given-names></name><name><surname>Cohen</surname><given-names>T</given-names></name><name><surname>Cooper</surname><given-names>B</given-names></name><etal></etal></person-group><article-title>Transmission dynamics and control of severe acute respiratory syndrome</article-title><source>Science</source><year>2003</year><volume>300</volume><fpage>1966</fpage><lpage>1970</lpage><pub-id pub-id-type="doi">10.1126/science.1086616</pub-id><pub-id pub-id-type="pmid">12766207</pub-id></element-citation></ref><ref id="CR8"><label>8</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dye</surname><given-names>C</given-names></name><name><surname>Gay</surname><given-names>N</given-names></name></person-group><article-title>Modelling the SARS epidemic</article-title><source>Science</source><year>2003</year><volume>300</volume><fpage>1884</fpage><lpage>1885</lpage><pub-id pub-id-type="doi">10.1126/science.1086925</pub-id><pub-id pub-id-type="pmid">12766208</pub-id></element-citation></ref><ref id="CR9"><label>9</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jia</surname><given-names>N</given-names></name><name><surname>Tsui</surname><given-names>L</given-names></name></person-group><article-title>Epidemic modelling using Sars as a case study</article-title><source>N Am Actuarial J</source><year>2005</year><volume>9</volume><fpage>28</fpage><lpage>42</lpage><pub-id pub-id-type="doi">10.1080/10920277.2005.10596223</pub-id></element-citation></ref><ref id="CR10"><label>10</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Watts</surname><given-names>D J</given-names></name><name><surname>Muhamad</surname><given-names>R</given-names></name><name><surname>Medina</surname><given-names>D C</given-names></name><etal></etal></person-group><article-title>Multiscale, resurgent epidemics in a hierarchical metapopulation model</article-title><source>Proc Natl Acad Sci</source><year>2005</year><volume>102</volume><fpage>11157</fpage><lpage>11162</lpage><pub-id pub-id-type="doi">10.1073/pnas.0501226102</pub-id><pub-id pub-id-type="pmid">16055564</pub-id></element-citation></ref><ref id="CR11"><label>11</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zhang</surname><given-names>Z B</given-names></name></person-group><article-title>The outbreak pattern of SARS cases in China as revealed by a mathematical model</article-title><source>Ecol Model</source><year>2007</year><volume>204</volume><fpage>420</fpage><lpage>426</lpage><pub-id pub-id-type="doi">10.1016/j.ecolmodel.2007.01.020</pub-id></element-citation></ref><ref id="CR12"><label>12</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kenah</surname><given-names>E</given-names></name><name><surname>Robins</surname><given-names>J M</given-names></name></person-group><article-title>Second look at the spread of epidemics on networks</article-title><source>Phys Rev E</source><year>2007</year><volume>76</volume><fpage>036113</fpage><pub-id pub-id-type="doi">10.1103/PhysRevE.76.036113</pub-id></element-citation></ref><ref id="CR13"><label>13</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bian</surname><given-names>L</given-names></name><name><surname>Liebner</surname><given-names>D</given-names></name></person-group><article-title>A network model for dispersion of communicable diseases</article-title><source>Trans GIS</source><year>2007</year><volume>11</volume><fpage>155</fpage><lpage>173</lpage><pub-id pub-id-type="doi">10.1111/j.1467-9671.2007.01039.x</pub-id></element-citation></ref><ref id="CR14"><label>14</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yu</surname><given-names>X L</given-names></name><name><surname>Wang</surname><given-names>X Y</given-names></name><name><surname>Zhang</surname><given-names>D M</given-names></name><etal></etal></person-group><article-title>Mathematical expressions for epidemics and immunization in small-world networks</article-title><source>Physica A</source><year>2008</year><volume>387</volume><fpage>1421</fpage><lpage>1430</lpage><pub-id pub-id-type="doi">10.1016/j.physa.2007.08.060</pub-id></element-citation></ref><ref id="CR15"><label>15</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dybiec</surname><given-names>B</given-names></name></person-group><article-title>SIR model of epidemic spread w ith accumulated exposure</article-title><source>The Eur Phys J B</source><year>2009</year><volume>67</volume><fpage>377</fpage><lpage>383</lpage><pub-id pub-id-type="doi">10.1140/epjb/e2008-00435-y</pub-id></element-citation></ref><ref id="CR16"><label>16</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dybiec</surname><given-names>B</given-names></name><name><surname>Kleczkowski</surname><given-names>A</given-names></name><name><surname>Gilligan</surname><given-names>C A</given-names></name></person-group><article-title>Modelling control of epidemics spreading by long-range interactions</article-title><source>J R Soc Interface</source><year>2009</year><volume>6</volume><fpage>941</fpage><lpage>950</lpage><pub-id pub-id-type="doi">10.1098/rsif.2008.0468</pub-id><pub-id pub-id-type="pmid">19126536</pub-id></element-citation></ref><ref id="CR17"><label>17</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Anderson</surname><given-names>R M</given-names></name><name><surname>May</surname><given-names>R M</given-names></name></person-group><source>Infectious Diseases of Humans</source><year>1991</year><publisher-loc>Oxford</publisher-loc><publisher-name>Oxford University Press</publisher-name></element-citation></ref><ref id="CR18"><label>18</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Mollison</surname><given-names>D</given-names></name></person-group><source>Epidemic Models</source><year>1995</year><publisher-loc>Cambridge</publisher-loc><publisher-name>Cambridge University Press</publisher-name></element-citation></ref><ref id="CR19"><label>19</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Edelstein-Keshet</surname><given-names>L</given-names></name></person-group><source>Mathematical Models in Biology</source><year>1988</year><publisher-loc>New York</publisher-loc><publisher-name>Random House</publisher-name></element-citation></ref><ref id="CR20"><label>20</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wu</surname><given-names>Z N</given-names></name></person-group><article-title>Prediction of the size distribution of secondary ejected droplets by crown splashing of droplets impinging on a solid wall</article-title><source>Probabilist Eng Mech</source><year>2003</year><volume>18</volume><fpage>241</fpage><lpage>249</lpage><pub-id pub-id-type="doi">10.1016/S0266-8920(03)00028-6</pub-id></element-citation></ref><ref id="CR21"><label>21</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Brauer</surname><given-names>F</given-names></name><name><surname>Castillo-Chavez</surname><given-names>C</given-names></name></person-group><source>Mathematical Models in Population Biology and Epidemiology</source><year>2001</year><publisher-loc>New York</publisher-loc><publisher-name>Springer</publisher-name></element-citation></ref><ref id="CR22"><label>22</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ahmed</surname><given-names>E</given-names></name><name><surname>Agiza</surname><given-names>H N</given-names></name></person-group><article-title>On modeling epidemics, including latency, incubation and variable susceptibility</article-title><source>Physica A</source><year>1998</year><volume>253</volume><fpage>347</fpage><lpage>352</lpage><pub-id pub-id-type="doi">10.1016/S0378-4371(97)00665-1</pub-id></element-citation></ref><ref id="CR23"><label>23</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Greenhalgh</surname><given-names>D</given-names></name><name><surname>Das</surname><given-names>P</given-names></name></person-group><article-title>Modeling epidemics with variable contact rates</article-title><source>Theor Population Biology</source><year>1995</year><volume>47</volume><fpage>129</fpage><lpage>179</lpage><pub-id pub-id-type="doi">10.1006/tpbi.1995.1006</pub-id></element-citation></ref><ref id="CR24"><label>24</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Weber</surname><given-names>A</given-names></name><name><surname>Weber</surname><given-names>M</given-names></name><name><surname>Milligan</surname><given-names>P</given-names></name></person-group><article-title>Modelling epidemics caused by respiratory syncytial virus</article-title><source>Mathematical Biosciences</source><year>2001</year><volume>172</volume><fpage>99</fpage><lpage>113</lpage><pub-id pub-id-type="doi">10.1016/S0025-5564(01)00066-9</pub-id></element-citation></ref><ref id="CR25"><label>25</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pybus</surname><given-names>O G</given-names></name><name><surname>Charleston</surname><given-names>M A</given-names></name><name><surname>Gupta</surname><given-names>S</given-names></name><etal></etal></person-group><article-title>The epidemic behavior of the hepatitis C virus</article-title><source>Science</source><year>2001</year><volume>292</volume><fpage>2323</fpage><lpage>2325</lpage><pub-id pub-id-type="doi">10.1126/science.1058321</pub-id><pub-id pub-id-type="pmid">11423661</pub-id></element-citation></ref><ref id="CR26"><label>26</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Anderson</surname><given-names>J D</given-names></name></person-group><source>Hypersonic and High Temperature Gas Dynamics</source><year>2006</year><publisher-loc>Virginia</publisher-loc><publisher-name>AIAA Education Series</publisher-name></element-citation></ref><ref id="CR27"><label>27</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Ziegler</surname><given-names>H</given-names></name></person-group><source>An Introduction to Thermomechanics</source><year>1983</year><publisher-loc>Amsterdam</publisher-loc><publisher-name>North-Holland Publisher</publisher-name></element-citation></ref><ref id="CR28"><label>28</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gao</surname><given-names>R B</given-names></name><name><surname>Cao</surname><given-names>B</given-names></name><name><surname>Hu</surname><given-names>Y W</given-names></name><etal></etal></person-group><article-title>Human infection with a novel avianorigin influenza a (H7N9) virus</article-title><source>N Eng J Med</source><year>2013</year><volume>368</volume><fpage>1888</fpage><lpage>1897</lpage><pub-id pub-id-type="doi">10.1056/NEJMoa1304459</pub-id></element-citation></ref><ref id="CR29"><label>29</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wen</surname><given-names>Y M</given-names></name><name><surname>Klenk</surname><given-names>H D</given-names></name></person-group><article-title>H7N9 avian influenza virus — search and research</article-title><source>Emerging Microbes Infections</source><year>2013</year><volume>2</volume><fpage>e18</fpage><pub-id pub-id-type="doi">10.1038/emi.2013.18</pub-id><pub-id pub-id-type="pmid">26038459</pub-id></element-citation></ref><ref id="CR30"><label>30</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>She</surname><given-names>Z S</given-names></name></person-group><source>A New Framework for Complex System</source><year>2012</year><publisher-loc>Beijing</publisher-loc><publisher-name>Science Presss</publisher-name></element-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Sante/explor/SrasV1/Data/Pmc/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 0004660 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Pmc/Corpus/biblio.hfd -nk 0004660 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Sante
|area= SrasV1
|flux= Pmc
|étape= Corpus
|type= RBID
|clé=
|texte=
}}
| This area was generated with Dilib version V0.6.33. |  |