Serveur d'exploration SRAS

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

Basic Knowledge and Developing Tendencies in Epidemic Dynamics

Identifieur interne : 000149 ( Pmc/Corpus ); précédent : 000148; suivant : 000150

Basic Knowledge and Developing Tendencies in Epidemic Dynamics

Auteurs :

Source :

RBID : PMC:7123007

Abstract

Summary

Infectious diseases have been a ferocious enemy since time immemorial. To prevent and control the spread of infectious diseases, epidemic dynamics has played an important role on investigating the transmission of infectious diseases, predicting the developing tendencies, estimating the key parameters from data published by health departments, understanding the transmission characteristics, and implementing the measures for prevention and control. In this chapter, some basic ideas of modelling the spread of infectious diseases, the main concepts of epidemic dynamics, and some developing tendencies in the study of epidemic dynamics are introduced, and some results with respect to the spread of SARS in China are given.


Url:
DOI: 10.1007/978-3-540-34426-1_2
PubMed: NONE
PubMed Central: 7123007

Links to Exploration step

PMC:7123007

Le document en format XML

<record>
<TEI>
<teiHeader>
<fileDesc>
<titleStmt>
<title xml:lang="en">Basic Knowledge and Developing Tendencies in Epidemic Dynamics</title>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">PMC</idno>
<idno type="pmc">7123007</idno>
<idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7123007</idno>
<idno type="RBID">PMC:7123007</idno>
<idno type="doi">10.1007/978-3-540-34426-1_2</idno>
<idno type="pmid">NONE</idno>
<date when="2007">2007</date>
<idno type="wicri:Area/Pmc/Corpus">000149</idno>
<idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000149</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title xml:lang="en" level="a" type="main">Basic Knowledge and Developing Tendencies in Epidemic Dynamics</title>
</analytic>
<series>
<title level="j">Mathematics for Life Science and Medicine</title>
<imprint>
<date when="2007">2007</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc>
<textClass></textClass>
</profileDesc>
</teiHeader>
<front>
<div type="abstract" xml:lang="en">
<title>Summary</title>
<p>Infectious diseases have been a ferocious enemy since time immemorial. To prevent and control the spread of infectious diseases, epidemic dynamics has played an important role on investigating the transmission of infectious diseases, predicting the developing tendencies, estimating the key parameters from data published by health departments, understanding the transmission characteristics, and implementing the measures for prevention and control. In this chapter, some basic ideas of modelling the spread of infectious diseases, the main concepts of epidemic dynamics, and some developing tendencies in the study of epidemic dynamics are introduced, and some results with respect to the spread of SARS in China are given.</p>
</div>
</front>
<back>
<div1 type="bibliography">
<listBibl>
<biblStruct>
<analytic>
<author>
<name sortKey="Allen, L J S" uniqKey="Allen L">L. J. S. Allen</name>
</author>
<author>
<name sortKey="Thrasher, D B" uniqKey="Thrasher D">D. B. Thrasher</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Allen, L J S" uniqKey="Allen L">L. J. S. Allen</name>
</author>
<author>
<name sortKey="Jones, M A" uniqKey="Jones M">M. A. Jones</name>
</author>
<author>
<name sortKey="Martin, C E" uniqKey="Martin C">C. E. Martin</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Anderson, R" uniqKey="Anderson R">R. Anderson</name>
</author>
<author>
<name sortKey="May, R" uniqKey="May R">R. May</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="Baily, N T J" uniqKey="Baily N">N. T. J. Baily</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Bainov, D D" uniqKey="Bainov D">D. D. Bainov</name>
</author>
<author>
<name sortKey="Simeonov, P S" uniqKey="Simeonov P">P. S. Simeonov</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Begon, M" uniqKey="Begon M">M. Begon</name>
</author>
<author>
<name sortKey="Bowers, R G" uniqKey="Bowers R">R. G. Bowers</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Begon, M" uniqKey="Begon M">M. Begon</name>
</author>
<author>
<name sortKey="Bowers, R G" uniqKey="Bowers R">R. G. Bowers</name>
</author>
<author>
<name sortKey="Kadianakis, N" uniqKey="Kadianakis N">N. Kadianakis</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Bowers, R G" uniqKey="Bowers R">R. G. Bowers</name>
</author>
<author>
<name sortKey="Begon, M" uniqKey="Begon M">M. Begon</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="Brauer, F" uniqKey="Brauer F">F. Brauer</name>
</author>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. van den Driessche</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Busenberg, S" uniqKey="Busenberg S">S. Busenberg</name>
</author>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. van den Driessche</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Busenberg, S" uniqKey="Busenberg S">S. Busenberg</name>
</author>
<author>
<name sortKey="Cooke, K" uniqKey="Cooke K">K. Cooke</name>
</author>
<author>
<name sortKey="Iannelli, M" uniqKey="Iannelli M">M. Iannelli</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Busenberg, S" uniqKey="Busenberg S">S. Busenberg</name>
</author>
<author>
<name sortKey="Iannelli, M" uniqKey="Iannelli M">M. Iannelli</name>
</author>
<author>
<name sortKey="Thieme, H R" uniqKey="Thieme H">H. R. Thieme</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Capasso, V" uniqKey="Capasso V">V. Capasso</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C. Castillo-Chavez</name>
</author>
<author>
<name sortKey="Huang, W Z" uniqKey="Huang W">W. Z. Huang</name>
</author>
<author>
<name sortKey="Li, J" uniqKey="Li J">J. Li</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C. Castillo-Chavez</name>
</author>
<author>
<name sortKey="Blower, S" uniqKey="Blower S">S. Blower</name>
</author>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. van den Driessche</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Cooke, K" uniqKey="Cooke K">K. Cooke</name>
</author>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. van den Driessche</name>
</author>
<author>
<name sortKey="Zou, X" uniqKey="Zou X">X. Zou</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="De Boer, R J" uniqKey="De Boer R">R. J. De Boer</name>
</author>
<author>
<name sortKey="Perelson, A S" uniqKey="Perelson A">A. S. Perelson</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Dietz, K" uniqKey="Dietz K">K. Dietz</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Dietz, K" uniqKey="Dietz K">K. Dietz</name>
</author>
<author>
<name sortKey="Schenzle, D" uniqKey="Schenzle D">D. Schenzle</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="D Nofri, A" uniqKey="D Nofri A">A. D’Onofri</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Dushoff, J" uniqKey="Dushoff J">J. Dushoff</name>
</author>
<author>
<name sortKey="Huang, W" uniqKey="Huang W">W. Huang</name>
</author>
<author>
<name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C. Castillo-Chavez</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Fan, M" uniqKey="Fan M">M. Fan</name>
</author>
<author>
<name sortKey="Li, M Y" uniqKey="Li M">M. Y. Li</name>
</author>
<author>
<name sortKey="Wang, K" uniqKey="Wang K">K. Wang</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Feng, Z" uniqKey="Feng Z">Z. Feng</name>
</author>
<author>
<name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C. Castillo-Chavez</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Feng, Z" uniqKey="Feng Z">Z. Feng</name>
</author>
<author>
<name sortKey="Thieme, H R" uniqKey="Thieme H">H. R. Thieme</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Feng, Z" uniqKey="Feng Z">Z. Feng</name>
</author>
<author>
<name sortKey="Thieme, H R" uniqKey="Thieme H">H. R. Thieme</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Guo, D J" uniqKey="Guo D">D. J. Guo</name>
</author>
<author>
<name sortKey="Sun, J X" uniqKey="Sun J">J. X. Sun</name>
</author>
<author>
<name sortKey="Zhao, Z L" uniqKey="Zhao Z">Z. L. Zhao</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hadeler, K" uniqKey="Hadeler K">K. Hadeler</name>
</author>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. van den Driessche</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hamer, W H" uniqKey="Hamer W">W. H. Hamer</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Han, L T" uniqKey="Han L">L. T. Han</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Han, L T" uniqKey="Han L">L. T. Han</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Shi, T" uniqKey="Shi T">T. Shi</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Han, L T" uniqKey="Han L">L. T. Han</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Hethcote, H M" uniqKey="Hethcote H">H. M. Hethcote</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="He, Z R" uniqKey="He Z">Z. R. He</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Heesterbeek, J A P" uniqKey="Heesterbeek J">J. A. P. Heesterbeek</name>
</author>
<author>
<name sortKey="Metz, J A J" uniqKey="Metz J">J. A. J. Metz</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hethcote, H" uniqKey="Hethcote H">H. Hethcote</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hethcote, H W" uniqKey="Hethcote H">H. W. Hethcote</name>
</author>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. van den Driessche</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hethcote, H W" uniqKey="Hethcote H">H. W. Hethcote</name>
</author>
<author>
<name sortKey="Yorke, J A" uniqKey="Yorke J">J. A. Yorke</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hethcote, H" uniqKey="Hethcote H">H. Hethcote</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Liao, S" uniqKey="Liao S">S. Liao</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Hoppensteadt, F" uniqKey="Hoppensteadt F">F. Hoppensteadt</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Iannelli, M" uniqKey="Iannelli M">M. Iannelli</name>
</author>
<author>
<name sortKey="Miller, F A" uniqKey="Miller F">F. A. Miller</name>
</author>
<author>
<name sortKey="Pugliese, A" uniqKey="Pugliese A">A. Pugliese</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Iannelli, M" uniqKey="Iannelli M">M. Iannelli</name>
</author>
<author>
<name sortKey="Kim, M Y" uniqKey="Kim M">M. Y. Kim</name>
</author>
<author>
<name sortKey="Park, J" uniqKey="Park J">J. Park</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Jin, Z" uniqKey="Jin Z">Z. Jin</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Jing, Z J" uniqKey="Jing Z">Z. J. Jing</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Kermack, W O" uniqKey="Kermack W">W. O. Kermack</name>
</author>
<author>
<name sortKey="Mckendrick, A G" uniqKey="Mckendrick A">A. G. McKendrick</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Kermack, W O" uniqKey="Kermack W">W. O. Kermack</name>
</author>
<author>
<name sortKey="Mckendrick, A G" uniqKey="Mckendrick A">A. G. McKendrick</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Lakshmikantham, V" uniqKey="Lakshmikantham V">V. Lakshmikantham</name>
</author>
<author>
<name sortKey="Bainov, D D" uniqKey="Bainov D">D. D. Bainov</name>
</author>
<author>
<name sortKey="Simeonov, P S" uniqKey="Simeonov P">P. S. Simeonov</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Langlais, M" uniqKey="Langlais M">M. Langlais</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, J Q" uniqKey="Li J">J. Q. Li</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, J Q" uniqKey="Li J">J. Q. Li</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, J Q" uniqKey="Li J">J. Q. Li</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, J Q" uniqKey="Li J">J. Q. Li</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, J" uniqKey="Li J">J. Li</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Blythe, S P" uniqKey="Blythe S">S. P. Blythe</name>
</author>
<author>
<name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C. Castillo-Chavez</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, M Y" uniqKey="Li M">M. Y. Li</name>
</author>
<author>
<name sortKey="Muldowney, J S" uniqKey="Muldowney J">J. S. Muldowney</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, M Y" uniqKey="Li M">M. Y. Li</name>
</author>
<author>
<name sortKey="Graef, J R" uniqKey="Graef J">J. R. Graef</name>
</author>
<author>
<name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, M Y" uniqKey="Li M">M. Y. Li</name>
</author>
<author>
<name sortKey="Muldowney, J S" uniqKey="Muldowney J">J. S. Muldowney</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, M Y" uniqKey="Li M">M. Y. Li</name>
</author>
<author>
<name sortKey="Smith, H L" uniqKey="Smith H">H. L. Smith</name>
</author>
<author>
<name sortKey="Wang, L" uniqKey="Wang L">L. Wang</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, X Z" uniqKey="Li X">X. Z. Li</name>
</author>
<author>
<name sortKey="Gupur, G" uniqKey="Gupur G">G. Gupur</name>
</author>
<author>
<name sortKey="Zhu, G T" uniqKey="Zhu G">G. T. Zhu</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Li, X Z" uniqKey="Li X">X. Z.. Li</name>
</author>
<author>
<name sortKey="Gupur, G" uniqKey="Gupur G">G. Gupur</name>
</author>
<author>
<name sortKey="Zhu, G T" uniqKey="Zhu G">G. T. Zhu</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Liu, H W" uniqKey="Liu H">H.-W. Liu</name>
</author>
<author>
<name sortKey="Xu, J" uniqKey="Xu J">J. Xu</name>
</author>
<author>
<name sortKey="Xu, Q M" uniqKey="Xu Q">Q. M. Xu</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Liu, W Min" uniqKey="Liu W">W.-min. Liu</name>
</author>
<author>
<name sortKey="Hethcote, H W" uniqKey="Hethcote H">H. W. Hethcote</name>
</author>
<author>
<name sortKey="Levin, S A" uniqKey="Levin S">S. A. Levin</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Liu, W Min" uniqKey="Liu W">W.-min. Liu</name>
</author>
<author>
<name sortKey="Levin, S A" uniqKey="Levin S">S. A. Levin</name>
</author>
<author>
<name sortKey="Iwasa, Y" uniqKey="Iwasa Y">Y. Iwasa</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Lizana, M" uniqKey="Lizana M">M. Lizana</name>
</author>
<author>
<name sortKey="Rivero, J" uniqKey="Rivero J">J. Rivero</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Lou, J" uniqKey="Lou J">J. Lou</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Li, J Q" uniqKey="Li J">J. Q. Li</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Lu, Z H" uniqKey="Lu Z">Z. H. Lu</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L. S. Chen</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Lu, Z H" uniqKey="Lu Z">Z. H. Lu</name>
</author>
<author>
<name sortKey="Gao, S J" uniqKey="Gao S">S. J. Gao</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L. S. Chen</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ma, J L" uniqKey="Ma J">J. L. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ma, W B" uniqKey="Ma W">W. B. Ma</name>
</author>
<author>
<name sortKey="Hara, T" uniqKey="Hara T">T. Hara</name>
</author>
<author>
<name sortKey="Takeuchi, Y" uniqKey="Takeuchi Y">Y. Takeuchi</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Zhou, Y C" uniqKey="Zhou Y">Y. C. Zhou</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Liu, J P" uniqKey="Liu J">J. P. Liu</name>
</author>
<author>
<name sortKey="Li, J" uniqKey="Li J">J. Li</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
<author>
<name sortKey="Zhou, Y C" uniqKey="Zhou Y">Y. C. Zhou</name>
</author>
<author>
<name sortKey="Wang, W D" uniqKey="Wang W">W. D. Wang</name>
</author>
<author>
<name sortKey="Jin, Z" uniqKey="Jin Z">Z. Jin</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Mena Lorca, J" uniqKey="Mena Lorca J">J. Mena-Lorca</name>
</author>
<author>
<name sortKey="Hethcote, H W" uniqKey="Hethcote H">H. W. Hethcote</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Miiller, J" uniqKey="Miiller J">J. Miiller</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Muldowney, J S" uniqKey="Muldowney J">J. S. Muldowney</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Pazy, A" uniqKey="Pazy A">A. Pazy</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Perelson, A S" uniqKey="Perelson A">A. S. Perelson</name>
</author>
<author>
<name sortKey="Kirschner, D E" uniqKey="Kirschner D">D. E. Kirschner</name>
</author>
<author>
<name sortKey="De Boer, R J" uniqKey="De Boer R">R. J. De Boer</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Culshaw, R V" uniqKey="Culshaw R">R. V. Culshaw</name>
</author>
<author>
<name sortKey="Ruan, S" uniqKey="Ruan S">S. Ruan</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Roberts, M G" uniqKey="Roberts M">M. G. Roberts</name>
</author>
<author>
<name sortKey="Kao, R R" uniqKey="Kao R">R. R. Kao</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ross, R" uniqKey="Ross R">R. Ross</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Ruan, S G" uniqKey="Ruan S">S. G. Ruan</name>
</author>
<author>
<name sortKey="Wang, W D" uniqKey="Wang W">W. D. Wang</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Shulgin, B" uniqKey="Shulgin B">B. Shulgin</name>
</author>
<author>
<name sortKey="Stone, L" uniqKey="Stone L">L. Stone</name>
</author>
<author>
<name sortKey="Agur, Z" uniqKey="Agur Z">Z. Agur</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Stone, L" uniqKey="Stone L">L. Stone</name>
</author>
<author>
<name sortKey="Shulgin, B" uniqKey="Shulgin B">B. Shulgin</name>
</author>
<author>
<name sortKey="Agur, Z" uniqKey="Agur Z">Z. Agur</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Van Den Driessche, P" uniqKey="Van Den Driessche P">P. Van den Driessche</name>
</author>
<author>
<name sortKey="Watmough, J" uniqKey="Watmough J">J. Watmough</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Venturino, E" uniqKey="Venturino E">E. Venturino</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Wang, W D" uniqKey="Wang W">W. D. Wang</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Wang, W D" uniqKey="Wang W">W. D. Wang</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Wang, W D" uniqKey="Wang W">W. D. Wang</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Wu, L I" uniqKey="Wu L">L.-I. Wu</name>
</author>
<author>
<name sortKey="Feng, Z" uniqKey="Feng Z">Z. Feng</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Xiao, Y N" uniqKey="Xiao Y">Y. N. Xiao</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L. S. Chen</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Xiao, Y N" uniqKey="Xiao Y">Y. N. Xiao</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L.. S. Chen</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Xiao, Y N" uniqKey="Xiao Y">Y. N. Xiao</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L.S. Chen</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Xiao, Y N" uniqKey="Xiao Y">Y. N. Xiao</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L. S. Chen</name>
</author>
<author>
<name sortKey="Ven Den Bosch, F" uniqKey="Ven Den Bosch F">F. ven den Bosch</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Xiao, Y N" uniqKey="Xiao Y">Y. N. Xiao</name>
</author>
<author>
<name sortKey="Chen, L S" uniqKey="Chen L">L. S. Chen</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Yuan, S" uniqKey="Yuan S">S. Yuan</name>
</author>
<author>
<name sortKey="Ma, Z" uniqKey="Ma Z">Z. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Yuan, S" uniqKey="Yuan S">S. Yuan</name>
</author>
<author>
<name sortKey="Ma, Z" uniqKey="Ma Z">Z. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Yuan, S" uniqKey="Yuan S">S. Yuan</name>
</author>
<author>
<name sortKey="Han, L" uniqKey="Han L">L. Han</name>
</author>
<author>
<name sortKey="Ma, Z" uniqKey="Ma Z">Z. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Yuan, S" uniqKey="Yuan S">S. Yuan</name>
</author>
<author>
<name sortKey="Ma, Z" uniqKey="Ma Z">Z. Ma</name>
</author>
<author>
<name sortKey="Jin, Z" uniqKey="Jin Z">Z. Jin</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Zhang, J" uniqKey="Zhang J">J. Zhang</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Zhou, Y C" uniqKey="Zhou Y">Y. C. Zhou</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Zhou, Y C" uniqKey="Zhou Y">Y. C. Zhou</name>
</author>
<author>
<name sortKey="Song, B J" uniqKey="Song B">B. J. Song</name>
</author>
<author>
<name sortKey="Ma, Z E" uniqKey="Ma Z">Z. E. Ma</name>
</author>
</analytic>
</biblStruct>
<biblStruct></biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Zhou, Y" uniqKey="Zhou Y">Y. Zhou</name>
</author>
<author>
<name sortKey="Lou, M Z" uniqKey="Lou M">M. Z. Lou</name>
</author>
<author>
<name sortKey="Lou, J" uniqKey="Lou J">J. Lou</name>
</author>
</analytic>
</biblStruct>
<biblStruct>
<analytic>
<author>
<name sortKey="Zhu, L Y" uniqKey="Zhu L">L. Y. Zhu</name>
</author>
<author>
<name sortKey="Zhou, Y C" uniqKey="Zhou Y">Y. C. Zhou</name>
</author>
</analytic>
</biblStruct>
</listBibl>
</div1>
</back>
</TEI>
<pmc article-type="chapter-article">
<pmc-dir>properties open_access</pmc-dir>
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">978-3-540-34426-1</journal-id>
<journal-id journal-id-type="doi">10.1007/978-3-540-34426-1</journal-id>
<journal-id journal-id-type="nlm-ta">Mathematics for Life Science and Medicine</journal-id>
<journal-title-group>
<journal-title>Mathematics for Life Science and Medicine</journal-title>
</journal-title-group>
<isbn publication-format="print">978-3-540-34425-4</isbn>
<isbn publication-format="electronic">978-3-540-34426-1</isbn>
</journal-meta>
<article-meta>
<article-id pub-id-type="pmc">7123007</article-id>
<article-id pub-id-type="publisher-id">2</article-id>
<article-id pub-id-type="doi">10.1007/978-3-540-34426-1_2</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Basic Knowledge and Developing Tendencies in Epidemic Dynamics</article-title>
</title-group>
<contrib-group content-type="book editors">
<contrib contrib-type="editor">
<name>
<surname>Takeuchi</surname>
<given-names>Yasuhiro</given-names>
</name>
<address>
<email>takeuchi@sys.eng.shizuoka.ac.jp</email>
</address>
<xref ref-type="aff" rid="Aff32">32</xref>
</contrib>
<contrib contrib-type="editor">
<name>
<surname>Iwasa</surname>
<given-names>Yoh</given-names>
</name>
<address>
<email>yiwasscb@mbox.nc.kyushu-u.ac.jp</email>
</address>
<xref ref-type="aff" rid="Aff33">33</xref>
</contrib>
<contrib contrib-type="editor">
<name>
<surname>Sato</surname>
<given-names>Kazunori</given-names>
</name>
<address>
<email>sato@sys.eng.shizuoka.ac.jp</email>
</address>
<xref ref-type="aff" rid="Aff32">32</xref>
</contrib>
<aff id="Aff32">
<label>32</label>
<institution-wrap>
<institution-id institution-id-type="GRID">grid.263536.7</institution-id>
<institution-id institution-id-type="ISNI">0000000106564913</institution-id>
<institution>Faculty of Engineering, Department of Systems Engineering,</institution>
<institution>Shizuoka University,</institution>
</institution-wrap>
Hamamatsu 3-5-1, 432-8561 Shizuoka, Japan</aff>
<aff id="Aff33">
<label>33</label>
<institution-wrap>
<institution-id institution-id-type="GRID">grid.177174.3</institution-id>
<institution-id institution-id-type="ISNI">0000000122424849</institution-id>
<institution>Department of Biology,</institution>
<institution>Kyushu University,</institution>
</institution-wrap>
812-8581 Fukuoka, Japan</aff>
</contrib-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Ma</surname>
<given-names>Zhien</given-names>
</name>
<address>
<email>zhma@mail.xjtu.edu.cn</email>
</address>
<xref ref-type="aff" rid="Aff34">34</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Jianquan</given-names>
</name>
<address>
<email>jianq_li@263.net</email>
</address>
<xref ref-type="aff" rid="Aff35">35</xref>
</contrib>
<aff id="Aff34">
<label>34</label>
<institution-wrap>
<institution-id institution-id-type="GRID">grid.43169.39</institution-id>
<institution-id institution-id-type="ISNI">0000000105991243</institution-id>
<institution>Department of Applied Mathematics,</institution>
<institution>Xi’an Jiaotong University,</institution>
</institution-wrap>
China</aff>
<aff id="Aff35">
<label>35</label>
<institution-wrap>
<institution-id institution-id-type="GRID">grid.440645.7</institution-id>
<institution>Department of Mathematics and Physics,</institution>
<institution>Air Force Engineering University,</institution>
</institution-wrap>
China</aff>
</contrib-group>
<pub-date pub-type="ppub">
<year>2007</year>
</pub-date>
<fpage>5</fpage>
<lpage>49</lpage>
<permissions>
<copyright-statement>© Springer-Verlag Berlin Heidelberg 2007</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">
<title>Summary</title>
<p>Infectious diseases have been a ferocious enemy since time immemorial. To prevent and control the spread of infectious diseases, epidemic dynamics has played an important role on investigating the transmission of infectious diseases, predicting the developing tendencies, estimating the key parameters from data published by health departments, understanding the transmission characteristics, and implementing the measures for prevention and control. In this chapter, some basic ideas of modelling the spread of infectious diseases, the main concepts of epidemic dynamics, and some developing tendencies in the study of epidemic dynamics are introduced, and some results with respect to the spread of SARS in China are given.</p>
</abstract>
<kwd-group xml:lang="en">
<title>Keywords</title>
<kwd>Severe Acute Respiratory Syndrome</kwd>
<kwd>Epidemic Model</kwd>
<kwd>Endemic Equilibrium</kwd>
<kwd>Basic Reproduction Number</kwd>
<kwd>Severe Acute Respiratory Syndrome</kwd>
</kwd-group>
<custom-meta-group>
<custom-meta>
<meta-name>issue-copyright-statement</meta-name>
<meta-value>© Springer-Verlag Berlin Heidelberg 2007</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<back>
<ref-list id="Bib1">
<title>References</title>
<ref id="CR1">
<label>1.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Allen</surname>
<given-names>L. J. S.</given-names>
</name>
<name>
<surname>Thrasher</surname>
<given-names>D. B.</given-names>
</name>
</person-group>
<article-title>The effects of vaccination in an age-dependent model for varicella and herpes zoster</article-title>
<source>IEEE Transactions on Automatic Control</source>
<year>1998</year>
<volume>43</volume>
<fpage>779</fpage>
<pub-id pub-id-type="doi">10.1109/9.679018</pub-id>
</element-citation>
</ref>
<ref id="CR2">
<label>2.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Allen</surname>
<given-names>L. J. S.</given-names>
</name>
<name>
<surname>Jones</surname>
<given-names>M. A.</given-names>
</name>
<name>
<surname>Martin</surname>
<given-names>C. E.</given-names>
</name>
</person-group>
<article-title>A Discrete-time model with vaccination for a measles epidemic</article-title>
<source>Math. Biosci.</source>
<year>1991</year>
<volume>105</volume>
<fpage>111</fpage>
<pub-id pub-id-type="doi">10.1016/0025-5564(91)90051-J</pub-id>
<pub-id pub-id-type="pmid">1806092</pub-id>
</element-citation>
</ref>
<ref id="CR3">
<label>3.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Anderson</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>May</surname>
<given-names>R.</given-names>
</name>
</person-group>
<source>Population Biology of infectious diseases</source>
<year>1982</year>
<publisher-loc>Berlin, Heidelberg, New York</publisher-loc>
<publisher-name>Spring-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR4">
<label>4.</label>
<element-citation publication-type="journal">
<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>
<article-title>The invasion, persistence, and spread of infectious diseases within animal and plant communities</article-title>
<source>Phil. Trans. R. Soc.</source>
<year>1986</year>
<volume>B314</volume>
<fpage>533</fpage>
</element-citation>
</ref>
<ref id="CR5">
<label>5.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Baily</surname>
<given-names>N. T. J.</given-names>
</name>
</person-group>
<source>The Mathematical theory of infectious disease</source>
<year>1975</year>
<edition>2nd edn</edition>
<publisher-loc>New York</publisher-loc>
<publisher-name>Hafner</publisher-name>
</element-citation>
</ref>
<ref id="CR6">
<label>6.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Bainov</surname>
<given-names>D. D.</given-names>
</name>
<name>
<surname>Simeonov</surname>
<given-names>P. S.</given-names>
</name>
</person-group>
<source>Impulsive Differential Equations: Asymptotic Properties of the solutions</source>
<year>1995</year>
<publisher-loc>New Jersey London</publisher-loc>
<publisher-name>World Scientific</publisher-name>
</element-citation>
</ref>
<ref id="CR7">
<label>7.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Begon</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Bowers</surname>
<given-names>R. G.</given-names>
</name>
</person-group>
<article-title>Host-host-pathogen models and microbial pest control: the effect of host self-regulation</article-title>
<source>J. Theor. Biol.</source>
<year>1995</year>
<volume>169</volume>
<fpage>275</fpage>
<pub-id pub-id-type="doi">10.1006/jtbi.1994.1148</pub-id>
</element-citation>
</ref>
<ref id="CR8">
<label>8.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Begon</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Bowers</surname>
<given-names>R. G.</given-names>
</name>
<name>
<surname>Kadianakis</surname>
<given-names>N.</given-names>
</name>
<etal></etal>
</person-group>
<article-title>Disease and community structure: the importance of host-regulation in a host-host-pathogen model</article-title>
<source>Am. Nat.</source>
<year>1992</year>
<volume>139</volume>
<fpage>1131</fpage>
<pub-id pub-id-type="doi">10.1086/285379</pub-id>
</element-citation>
</ref>
<ref id="CR9">
<label>9.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bowers</surname>
<given-names>R. G.</given-names>
</name>
<name>
<surname>Begon</surname>
<given-names>M.</given-names>
</name>
</person-group>
<article-title>A host-pathogen model with free living infective stage, applicable to microbial pest control</article-title>
<source>J. Theor. Biol.</source>
<year>1991</year>
<volume>148</volume>
<fpage>305</fpage>
<pub-id pub-id-type="doi">10.1016/S0022-5193(05)80240-1</pub-id>
<pub-id pub-id-type="pmid">2016897</pub-id>
</element-citation>
</ref>
<ref id="CR10">
<label>10.</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>
<person-group person-group-type="editor">
<name>
<surname>Marsden</surname>
<given-names>J. E.</given-names>
</name>
<name>
<surname>Sirovich</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Golubitsky</surname>
<given-names>M.</given-names>
</name>
</person-group>
<article-title>Mathematical Models in Population Biology and Epidemiology</article-title>
<source>Texts in Applied Mathematics</source>
<year>2001</year>
<publisher-loc>New York Berlin Heidelberg</publisher-loc>
<publisher-name>Springer-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR11">
<label>11.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Brauer</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>van den Driessche</surname>
<given-names>P.</given-names>
</name>
</person-group>
<article-title>Models for transmission of disease with immigration of infectives</article-title>
<source>Math. Biosci.</source>
<year>2001</year>
<volume>171</volume>
<fpage>143</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(01)00057-8</pub-id>
<pub-id pub-id-type="pmid">11395048</pub-id>
</element-citation>
</ref>
<ref id="CR12">
<label>12.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Busenberg</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>van den Driessche</surname>
<given-names>P.</given-names>
</name>
</person-group>
<article-title>Analysis of a disease transmission model in a population with varying size</article-title>
<source>J. Math. Biol.</source>
<year>1990</year>
<volume>28</volume>
<fpage>257</fpage>
<pub-id pub-id-type="doi">10.1007/BF00178776</pub-id>
<pub-id pub-id-type="pmid">2332704</pub-id>
</element-citation>
</ref>
<ref id="CR13">
<label>13.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Busenberg</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Cooke</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Iannelli</surname>
<given-names>M.</given-names>
</name>
</person-group>
<article-title>Endemic, thresholds and stability in a case of age-structured epidemics</article-title>
<source>SIAM J. Appl. Math.</source>
<year>1988</year>
<volume>48</volume>
<fpage>1379</fpage>
<pub-id pub-id-type="doi">10.1137/0148085</pub-id>
</element-citation>
</ref>
<ref id="CR14">
<label>14.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Busenberg</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Iannelli</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Thieme</surname>
<given-names>H. R.</given-names>
</name>
</person-group>
<article-title>Global behavior of an age-structed epidemic model</article-title>
<source>SIAM J. Math. Anal.</source>
<year>1991</year>
<volume>22</volume>
<fpage>1065</fpage>
<pub-id pub-id-type="doi">10.1137/0522069</pub-id>
</element-citation>
</ref>
<ref id="CR15">
<label>15.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Capasso</surname>
<given-names>V.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>Mathematical Structures of Epidemic systems</article-title>
<source>Lecture Notes in Biomathematics</source>
<year>1993</year>
<publisher-loc>Heidelberg</publisher-loc>
<publisher-name>Springer-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR16">
<label>16.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>W. Z.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>Competitive exclusion in gonorrhea models and other sexually transmitted diseases</article-title>
<source>SIAM J. Appl. Math.</source>
<year>1996</year>
<volume>56</volume>
<fpage>494</fpage>
<pub-id pub-id-type="doi">10.1137/S003613999325419X</pub-id>
</element-citation>
</ref>
<ref id="CR17">
<label>17.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Blower</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>van den Driessche</surname>
<given-names>P.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>Mathematical Approaches for Emerging Infectious Diseases</article-title>
<source>The IMA volumes in mathematics and its applications</source>
<year>2002</year>
<publisher-loc>New York Berlin Heidelberg</publisher-loc>
<publisher-name>Springer-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR18">
<label>18.</label>
<mixed-citation publication-type="other">Chowell, G., P. W. Fenimore, M. A. Castillo-Garsow and C. Castillo-Chavez (2003), SARS outbreaks in Ontario, Hong Kong, and Singapore: the role of diagnosis and isolation as a control mechanism, Los Alamos Unclassified Report LA-UR-03-2653.</mixed-citation>
</ref>
<ref id="CR19">
<label>19.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cooke</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>van den Driessche</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Zou</surname>
<given-names>X.</given-names>
</name>
</person-group>
<article-title>Interaction of maturation delay and nonlinear birth in population and epidemic models</article-title>
<source>J. Math. Biol.</source>
<year>1999</year>
<volume>39</volume>
<fpage>332</fpage>
<pub-id pub-id-type="doi">10.1007/s002850050194</pub-id>
<pub-id pub-id-type="pmid">10550577</pub-id>
</element-citation>
</ref>
<ref id="CR20">
<label>20.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>De Boer</surname>
<given-names>R. J.</given-names>
</name>
<name>
<surname>Perelson</surname>
<given-names>A. S.</given-names>
</name>
</person-group>
<article-title>Target cell limited and immune control models of HIV infection: a comparison</article-title>
<source>J. Theor. Biol.</source>
<year>1998</year>
<volume>190</volume>
<fpage>201</fpage>
<pub-id pub-id-type="doi">10.1006/jtbi.1997.0548</pub-id>
<pub-id pub-id-type="pmid">9514649</pub-id>
</element-citation>
</ref>
<ref id="CR21">
<label>21.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Dietz</surname>
<given-names>K.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>Overall population patterns in the transmission cycle of infectious disease agents</article-title>
<source>Population Biology of infectious disease</source>
<year>1982</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>Dietz</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Schenzle</surname>
<given-names>D.</given-names>
</name>
</person-group>
<article-title>Proportionate mixing models for age-dependent infection transmission</article-title>
<source>J. Math. Biol.</source>
<year>1985</year>
<volume>22</volume>
<fpage>117</fpage>
<pub-id pub-id-type="doi">10.1007/BF00276550</pub-id>
<pub-id pub-id-type="pmid">3926925</pub-id>
</element-citation>
</ref>
<ref id="CR23">
<label>23.</label>
<mixed-citation publication-type="other">Donnelly, C. A., et al. (2003), Epidemiological determination of spread of causal agent of severe acute respiratory syndrome in Hong Kong. The Lancent, Publish online May 7, http://image.thelacent.com/extras/03 art 4453 web.psf.</mixed-citation>
</ref>
<ref id="CR24">
<label>24.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>D’Onofri</surname>
<given-names>A.</given-names>
</name>
</person-group>
<article-title>Stability properties of pulse vaccination strategy in SEIR epidemic model</article-title>
<source>Math. Biosci.</source>
<year>2002</year>
<volume>179</volume>
<fpage>57</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(02)00095-0</pub-id>
<pub-id pub-id-type="pmid">12047921</pub-id>
</element-citation>
</ref>
<ref id="CR25">
<label>25.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dushoff</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>Backward bifurcation and catastrophe in simple models of fatal disease</article-title>
<source>J. Math. Biol.</source>
<year>1998</year>
<volume>36</volume>
<fpage>227</fpage>
<pub-id pub-id-type="doi">10.1007/s002850050099</pub-id>
<pub-id pub-id-type="pmid">9528119</pub-id>
</element-citation>
</ref>
<ref id="CR26">
<label>26.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Fan</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>M. Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>K.</given-names>
</name>
</person-group>
<article-title>Global stability of an SEIS epidemic model with recruitment and a varying total population size</article-title>
<source>Math. Biosci.</source>
<year>2001</year>
<volume>170</volume>
<fpage>199</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(00)00067-5</pub-id>
<pub-id pub-id-type="pmid">11292499</pub-id>
</element-citation>
</ref>
<ref id="CR27">
<label>27.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Feng</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>A model for tuberculosis with exogenous reinfection</article-title>
<source>Theoret. Popul. Biol.</source>
<year>2000</year>
<volume>57</volume>
<fpage>235</fpage>
<pub-id pub-id-type="doi">10.1006/tpbi.2000.1451</pub-id>
<pub-id pub-id-type="pmid">10828216</pub-id>
</element-citation>
</ref>
<ref id="CR28">
<label>28.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Feng</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Thieme</surname>
<given-names>H. R.</given-names>
</name>
</person-group>
<article-title>Endemic models with arbitrarily distributed periods of infection, I: general theory</article-title>
<source>SIAM J. Appl. Math.</source>
<year>2003</year>
<volume>61</volume>
<fpage>803</fpage>
<pub-id pub-id-type="doi">10.1137/S0036139998347834</pub-id>
</element-citation>
</ref>
<ref id="CR29">
<label>29.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Feng</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Thieme</surname>
<given-names>H. R.</given-names>
</name>
</person-group>
<article-title>Endemic models with arbitrarily distributed periods of infection, II: fast disease dynamics and permanent recovery</article-title>
<source>SIAM J. Appl. Math.</source>
<year>2003</year>
<volume>61</volume>
<fpage>983</fpage>
<pub-id pub-id-type="doi">10.1137/S0036139998347846</pub-id>
</element-citation>
</ref>
<ref id="CR30">
<label>30.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Guo</surname>
<given-names>D. J.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>J. X.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>Z. L.</given-names>
</name>
</person-group>
<source>Methods of Nonlinear Scientific Functionals</source>
<year>1995</year>
<publisher-loc>Jinan</publisher-loc>
<publisher-name>Shandong Scientific Press</publisher-name>
</element-citation>
</ref>
<ref id="CR31">
<label>31.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hadeler</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>van den Driessche</surname>
<given-names>P.</given-names>
</name>
</person-group>
<article-title>Backward bifurcation in epidemic control</article-title>
<source>Math. Biosci.</source>
<year>1997</year>
<volume>146</volume>
<fpage>15</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(97)00027-8</pub-id>
<pub-id pub-id-type="pmid">9357292</pub-id>
</element-citation>
</ref>
<ref id="CR32">
<label>32.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hamer</surname>
<given-names>W. H.</given-names>
</name>
</person-group>
<article-title>Epidemic disease in England</article-title>
<source>Lancet</source>
<year>1906</year>
<volume>1</volume>
<fpage>733</fpage>
</element-citation>
</ref>
<ref id="CR33">
<label>33.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Han</surname>
<given-names>L. T.</given-names>
</name>
</person-group>
<source>Study on epidemic models of two interaction species</source>
<year>2002</year>
<publisher-loc>Xi’an, China</publisher-loc>
<publisher-name>Xi’an Jiaotong University</publisher-name>
</element-citation>
</ref>
<ref id="CR34">
<label>34.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Han</surname>
<given-names>L. T.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>T.</given-names>
</name>
</person-group>
<article-title>An SIRS epidemic model of two competitive species</article-title>
<source>Mathl. Comput. Modelling</source>
<year>2003</year>
<volume>37</volume>
<fpage>87</fpage>
<pub-id pub-id-type="doi">10.1016/S0895-7177(03)80008-0</pub-id>
</element-citation>
</ref>
<ref id="CR35">
<label>35.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Han</surname>
<given-names>L. T.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Hethcote</surname>
<given-names>H. M.</given-names>
</name>
</person-group>
<article-title>Four predator prey model with infectious diseases</article-title>
<source>Mathl. Comput. Modelling</source>
<year>2001</year>
<volume>34</volume>
<fpage>849</fpage>
<pub-id pub-id-type="doi">10.1016/S0895-7177(01)00104-2</pub-id>
</element-citation>
</ref>
<ref id="CR36">
<label>36.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>He</surname>
<given-names>Z. R.</given-names>
</name>
</person-group>
<source>Optimal control of population dynamical systems with agestructure</source>
<year>2000</year>
<publisher-loc>Xi’an, China</publisher-loc>
<publisher-name>Xi’an Jiaotong University</publisher-name>
</element-citation>
</ref>
<ref id="CR37">
<label>37.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Heesterbeek</surname>
<given-names>J. A. P.</given-names>
</name>
<name>
<surname>Metz</surname>
<given-names>J. A. J.</given-names>
</name>
</person-group>
<article-title>The saturating contact rate in marrige and epidemic models</article-title>
<source>J. Math. Biol.</source>
<year>1993</year>
<volume>31</volume>
<fpage>529</fpage>
<pub-id pub-id-type="doi">10.1007/BF00173891</pub-id>
<pub-id pub-id-type="pmid">8336087</pub-id>
</element-citation>
</ref>
<ref id="CR38">
<label>38.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hethcote</surname>
<given-names>H.</given-names>
</name>
</person-group>
<article-title>Qualitative analysis of communicable disease models</article-title>
<source>Math. Biosci.</source>
<year>1976</year>
<volume>28</volume>
<fpage>335</fpage>
<pub-id pub-id-type="doi">10.1016/0025-5564(76)90132-2</pub-id>
</element-citation>
</ref>
<ref id="CR39">
<label>39.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hethcote</surname>
<given-names>H. W.</given-names>
</name>
<name>
<surname>van den Driessche</surname>
<given-names>P.</given-names>
</name>
</person-group>
<article-title>An SIS epidemic model with variable population size and a delay</article-title>
<source>J. Math. Biol.</source>
<year>1995</year>
<volume>34</volume>
<fpage>177</fpage>
<pub-id pub-id-type="doi">10.1007/BF00178772</pub-id>
<pub-id pub-id-type="pmid">8576654</pub-id>
</element-citation>
</ref>
<ref id="CR40">
<label>40.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Hethcote</surname>
<given-names>H. W.</given-names>
</name>
<name>
<surname>Yorke</surname>
<given-names>J. A.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Hethcote</surname>
<given-names>H. W.</given-names>
</name>
</person-group>
<article-title>Gonorrhea transmission dynamics and control</article-title>
<source>Lecture Notes Biomathematics</source>
<year>1984</year>
<publisher-loc>Berlin-Heidelberg-New York</publisher-loc>
<publisher-name>Springer-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR41">
<label>41.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hethcote</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>S.</given-names>
</name>
</person-group>
<article-title>Effects of quarantine in six endemic models for infectious diseases</article-title>
<source>Math. Biosci.</source>
<year>2002</year>
<volume>180</volume>
<fpage>141</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(02)00111-6</pub-id>
<pub-id pub-id-type="pmid">12387921</pub-id>
</element-citation>
</ref>
<ref id="CR42">
<label>42.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hoppensteadt</surname>
<given-names>F.</given-names>
</name>
</person-group>
<article-title>An age dependent epidemic model</article-title>
<source>J. Franklin Inst.</source>
<year>1974</year>
<volume>197</volume>
<fpage>325</fpage>
<pub-id pub-id-type="doi">10.1016/0016-0032(74)90037-4</pub-id>
</element-citation>
</ref>
<ref id="CR43">
<label>43.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Iannelli</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Miller</surname>
<given-names>F. A.</given-names>
</name>
<name>
<surname>Pugliese</surname>
<given-names>A.</given-names>
</name>
</person-group>
<article-title>Analytic and numerical results for the age-structured SIS epidemic model with mixed inter-intracohort transmission</article-title>
<source>SIAM J. Math. Anal.</source>
<year>1992</year>
<volume>23</volume>
<fpage>662</fpage>
<pub-id pub-id-type="doi">10.1137/0523034</pub-id>
</element-citation>
</ref>
<ref id="CR44">
<label>44.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Iannelli</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Kim</surname>
<given-names>M. Y.</given-names>
</name>
<name>
<surname>Park</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>Asymptotic behavior for an SIS epidemic model and its approximation</article-title>
<source>Nonlinear Analysis: ATM</source>
<year>1999</year>
<volume>35</volume>
<fpage>797</fpage>
<pub-id pub-id-type="doi">10.1016/S0362-546X(97)00597-X</pub-id>
</element-citation>
</ref>
<ref id="CR45">
<label>45.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Jin</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<source>The study for ecological and epidemic models influenced by impulses</source>
<year>2001</year>
<publisher-loc>Xi’an, China</publisher-loc>
<publisher-name>Xi’an Jiaotong University</publisher-name>
</element-citation>
</ref>
<ref id="CR46">
<label>46.</label>
<mixed-citation publication-type="other">Jin, Z. and Z. E. Ma, Epidemic models with continuous and impulse vaccination, to appear.</mixed-citation>
</ref>
<ref id="CR47">
<label>47.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jing</surname>
<given-names>Z. J.</given-names>
</name>
</person-group>
<article-title>Mathematics and AIDS</article-title>
<source>Practice and Understanding of Mathematics</source>
<year>1990</year>
<volume>20</volume>
<fpage>47</fpage>
</element-citation>
</ref>
<ref id="CR48">
<label>48.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kermack</surname>
<given-names>W. O.</given-names>
</name>
<name>
<surname>McKendrick</surname>
<given-names>A. G.</given-names>
</name>
</person-group>
<article-title>Contributions to the mathematical theory of epidemics</article-title>
<source>Proc. Roy. Soc.</source>
<year>1932</year>
<volume>138</volume>
<fpage>55</fpage>
</element-citation>
</ref>
<ref id="CR49">
<label>49.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kermack</surname>
<given-names>W. O.</given-names>
</name>
<name>
<surname>McKendrick</surname>
<given-names>A. G.</given-names>
</name>
</person-group>
<article-title>Contributions to the mathematical theory of epidemics</article-title>
<source>Proc. Roy. Soc.</source>
<year>1927</year>
<volume>115</volume>
<fpage>700</fpage>
</element-citation>
</ref>
<ref id="CR50">
<label>50.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Lakshmikantham</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Bainov</surname>
<given-names>D. D.</given-names>
</name>
<name>
<surname>Simeonov</surname>
<given-names>P. S.</given-names>
</name>
</person-group>
<source>Theory of Impulsive Differential Equations</source>
<year>1989</year>
<publisher-loc>London</publisher-loc>
<publisher-name>World Scientific Press</publisher-name>
</element-citation>
</ref>
<ref id="CR51">
<label>51.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Langlais</surname>
<given-names>M.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>A mathematical analysis of the SIS intra-cohort model with age-structure</article-title>
<source>Mathematical Population Dynamics</source>
<year>1995</year>
<publisher-loc>Winning, Canada</publisher-loc>
<publisher-name>Wuerz Publishing Ltd.</publisher-name>
<fpage>103</fpage>
<lpage>117</lpage>
</element-citation>
</ref>
<ref id="CR52">
<label>52.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>J. Q.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<article-title>Qualitative analysis of an epidemic model with vaccination</article-title>
<source>Annals of Differential Equations</source>
<year>2003</year>
<volume>19</volume>
<fpage>34</fpage>
</element-citation>
</ref>
<ref id="CR53">
<label>53.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>J. Q.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<article-title>Global analysis of SIS epidemic models with variable total population size</article-title>
<source>Mathl. Comput. Modelling</source>
<year>2004</year>
<volume>39</volume>
<fpage>1231</fpage>
<pub-id pub-id-type="doi">10.1016/j.mcm.2004.06.004</pub-id>
</element-citation>
</ref>
<ref id="CR54">
<label>54.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>J. Q.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<article-title>Stability analysis for SIS epidemic models with vaccination and constant population size</article-title>
<source>Discrete and Continuous Dynamical Systems: Series B</source>
<year>2004</year>
<volume>4</volume>
<fpage>637</fpage>
</element-citation>
</ref>
<ref id="CR55">
<label>55.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>J. Q.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<article-title>Qualitative analyses of SIS epidemic model with vaccination and varying total population size</article-title>
<source>Mathl. Comput. Modelling</source>
<year>2002</year>
<volume>35</volume>
<fpage>1235</fpage>
<pub-id pub-id-type="doi">10.1016/S0895-7177(02)00082-1</pub-id>
</element-citation>
</ref>
<ref id="CR56">
<label>56.</label>
<mixed-citation publication-type="other">Li, J. Q. and Z. E. Ma, Global stability of two epidemic models with vaccination, to appear</mixed-citation>
</ref>
<ref id="CR57">
<label>57.</label>
<mixed-citation publication-type="other">Li, J. Q., Z. E. Ma and Y. C. Zhou, Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria, to appear.</mixed-citation>
</ref>
<ref id="CR58">
<label>58.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Blythe</surname>
<given-names>S. P.</given-names>
</name>
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>On coexistence of pathogens in a class of sexually transmitted diseases models</article-title>
<source>J. Math. Biol.</source>
<year>2003</year>
<volume>47</volume>
<fpage>547</fpage>
<pub-id pub-id-type="doi">10.1007/s00285-003-0235-5</pub-id>
<pub-id pub-id-type="pmid">14618379</pub-id>
</element-citation>
</ref>
<ref id="CR59">
<label>59.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>M. Y.</given-names>
</name>
<name>
<surname>Muldowney</surname>
<given-names>J. S.</given-names>
</name>
</person-group>
<article-title>Global stability for the SEIR in epidemiology</article-title>
<source>Math. Biosci.</source>
<year>1995</year>
<volume>125</volume>
<fpage>155</fpage>
<pub-id pub-id-type="doi">10.1016/0025-5564(95)92756-5</pub-id>
<pub-id pub-id-type="pmid">7881192</pub-id>
</element-citation>
</ref>
<ref id="CR60">
<label>60.</label>
<mixed-citation publication-type="other">Li, M. Y. and L. Wang, Global stability in some SEIR epidemic models, to appear.</mixed-citation>
</ref>
<ref id="CR61">
<label>61.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>M. Y.</given-names>
</name>
<name>
<surname>Graef</surname>
<given-names>J. R.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
<etal></etal>
</person-group>
<article-title>Global dynamics of a SEIR model with varying total population size</article-title>
<source>Math. Biosci.</source>
<year>1999</year>
<volume>160</volume>
<fpage>191</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(99)00030-9</pub-id>
<pub-id pub-id-type="pmid">10472754</pub-id>
</element-citation>
</ref>
<ref id="CR62">
<label>62.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>M. Y.</given-names>
</name>
<name>
<surname>Muldowney</surname>
<given-names>J. S.</given-names>
</name>
</person-group>
<article-title>A geometric approach to the global stability problems</article-title>
<source>SIAM J. Math. Anal.</source>
<year>1996</year>
<volume>27</volume>
<fpage>1070</fpage>
<pub-id pub-id-type="doi">10.1137/S0036141094266449</pub-id>
</element-citation>
</ref>
<ref id="CR63">
<label>63.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>M. Y.</given-names>
</name>
<name>
<surname>Smith</surname>
<given-names>H. L.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
</person-group>
<article-title>Global dynamics of an SEIR epidemic model with vertical transmission</article-title>
<source>SIAM J. Appl. Math.</source>
<year>2001</year>
<volume>62</volume>
<fpage>58</fpage>
<pub-id pub-id-type="doi">10.1137/S0036139999359860</pub-id>
</element-citation>
</ref>
<ref id="CR64">
<label>64.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>X. Z.</given-names>
</name>
<name>
<surname>Gupur</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>G. T.</given-names>
</name>
</person-group>
<article-title>Threshold and stability results for an age-structured SEIR epidemic model</article-title>
<source>Comp. Math. Appl.</source>
<year>2001</year>
<volume>42</volume>
<fpage>883</fpage>
<pub-id pub-id-type="doi">10.1016/S0898-1221(01)00206-1</pub-id>
</element-citation>
</ref>
<ref id="CR65">
<label>65.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>X. Z..</given-names>
</name>
<name>
<surname>Gupur</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>G. T.</given-names>
</name>
</person-group>
<source>Mathematical Theory of Age-Structured Epidemic Dynamics</source>
<year>2003</year>
<publisher-loc>Hertfordshire</publisher-loc>
<publisher-name>Research Information Ltd.</publisher-name>
</element-citation>
</ref>
<ref id="CR66">
<label>66.</label>
<mixed-citation publication-type="other">Lipsitch, M., et al. (2003), Transmission dynamics and control of severe acute respiratory syndrome, Published online May 23, 2003; 10.1126/science. 1086616 (Science Express Reports).</mixed-citation>
</ref>
<ref id="CR67">
<label>67.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>H.-W.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>Q. M.</given-names>
</name>
</person-group>
<article-title>SIS epidemic models with continuous vaccination and age structure</article-title>
<source>Chinese J. Engin. Math.</source>
<year>2002</year>
<volume>19</volume>
<fpage>25</fpage>
<pub-id pub-id-type="doi">10.1007/BF02889680</pub-id>
</element-citation>
</ref>
<ref id="CR68">
<label>68.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>W.-min.</given-names>
</name>
<name>
<surname>Hethcote</surname>
<given-names>H. W.</given-names>
</name>
<name>
<surname>Levin</surname>
<given-names>S. A.</given-names>
</name>
</person-group>
<article-title>Dynamical behavior of epidemiological model with nonlinear incidence rates</article-title>
<source>J. Math. Biol.</source>
<year>1987</year>
<volume>25</volume>
<fpage>359</fpage>
<pub-id pub-id-type="doi">10.1007/BF00277162</pub-id>
<pub-id pub-id-type="pmid">3668394</pub-id>
</element-citation>
</ref>
<ref id="CR69">
<label>69.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>W.-min.</given-names>
</name>
<name>
<surname>Levin</surname>
<given-names>S. A.</given-names>
</name>
<name>
<surname>Iwasa</surname>
<given-names>Y.</given-names>
</name>
</person-group>
<article-title>Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models</article-title>
<source>J. Math. Biol.</source>
<year>1986</year>
<volume>23</volume>
<fpage>187</fpage>
<pub-id pub-id-type="doi">10.1007/BF00276956</pub-id>
<pub-id pub-id-type="pmid">3958634</pub-id>
</element-citation>
</ref>
<ref id="CR70">
<label>70.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lizana</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Rivero</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>Multiparametric bifurcation for a model in epidemiology</article-title>
<source>J. Math. Biol.</source>
<year>1996</year>
<volume>35</volume>
<fpage>21</fpage>
<pub-id pub-id-type="doi">10.1007/s002850050040</pub-id>
<pub-id pub-id-type="pmid">9002240</pub-id>
</element-citation>
</ref>
<ref id="CR71">
<label>71.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lou</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>J. Q.</given-names>
</name>
<etal></etal>
</person-group>
<article-title>The impact of the CD8+ cell non-cytotoxic antiviral response (CNAR) and cytotoxic T lymphocyte (CTL) activity in a cell-to-cell spread model for HIV-1 that includes a time delay</article-title>
<source>Journal of Biological Systems</source>
<year>2004</year>
<volume>12</volume>
<fpage>73</fpage>
<pub-id pub-id-type="doi">10.1142/S0218339004001038</pub-id>
</element-citation>
</ref>
<ref id="CR72">
<label>72.</label>
<mixed-citation publication-type="other">Lou, J., Z. E. Ma and Y. M. Shao, et al. (2004b), Modelling the interaction of T cells, antigen presenting cells and HIV in vivo, to appear in Comput. Math. Appl.</mixed-citation>
</ref>
<ref id="CR73">
<label>73.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Lu</surname>
<given-names>Z. H.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L. S.</given-names>
</name>
</person-group>
<article-title>Threshold theory of a nonautonomous SIS-infectious diseases model with logistic species growth</article-title>
<source>Advanced topics in biomathematics, Proc. of ICMB’97’ Hangzhou, China</source>
<year>1998</year>
<publisher-loc>Singapore</publisher-loc>
<publisher-name>World Scientific Press</publisher-name>
</element-citation>
</ref>
<ref id="CR74">
<label>74.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lu</surname>
<given-names>Z. H.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>S. J.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L. S.</given-names>
</name>
</person-group>
<article-title>Analysis of an SI epidemic model with nonlinear transmission and stage structure</article-title>
<source>Acta Math. Scientia</source>
<year>2003</year>
<volume>4</volume>
<fpage>440</fpage>
</element-citation>
</ref>
<ref id="CR75">
<label>75.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>J. L.</given-names>
</name>
</person-group>
<source>Study of threshold of nonautonomous infectious diseases models</source>
<year>2002</year>
<publisher-loc>Xi’an, China</publisher-loc>
<publisher-name>Xi’an Jiaotong University</publisher-name>
</element-citation>
</ref>
<ref id="CR76">
<label>76.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>W. B.</given-names>
</name>
<name>
<surname>Hara</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Takeuchi</surname>
<given-names>Y.</given-names>
</name>
<etal></etal>
</person-group>
<article-title>Permanence of an SIR epidemic model with distributed time delays</article-title>
<source>Tohoku Math.</source>
<year>2002</year>
<volume>54</volume>
<fpage>365</fpage>
</element-citation>
</ref>
<ref id="CR77">
<label>77.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Y. C.</given-names>
</name>
</person-group>
<source>Methods of Qualitativeness and Stability for Ordinary Differential Equations</source>
<year>2001</year>
<publisher-loc>Beijing</publisher-loc>
<publisher-name>Science Press</publisher-name>
</element-citation>
</ref>
<ref id="CR78">
<label>78.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>J. P.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>Stability analysis for differential infectivity epidemic models</article-title>
<source>Nonlinear Analysis: RWA</source>
<year>2003</year>
<volume>4</volume>
<fpage>841</fpage>
<pub-id pub-id-type="doi">10.1016/S1468-1218(03)00019-1</pub-id>
</element-citation>
</ref>
<ref id="CR79">
<label>79.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Y. C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>W. D.</given-names>
</name>
<name>
<surname>Jin</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<source>Mathematical Modelling and Study of Epidemic Dynamics</source>
<year>2004</year>
<publisher-loc>Beijing</publisher-loc>
<publisher-name>Science Press</publisher-name>
</element-citation>
</ref>
<ref id="CR80">
<label>80.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mena-Lorca</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Hethcote</surname>
<given-names>H. W.</given-names>
</name>
</person-group>
<article-title>Dynamic models of infectious diseases as regulators of population sizes</article-title>
<source>J. Math. Boil.</source>
<year>1992</year>
<volume>30</volume>
<fpage>693</fpage>
</element-citation>
</ref>
<ref id="CR81">
<label>81.</label>
<mixed-citation publication-type="other">MHC, Available from http://168.160.244.167/sarsmap.</mixed-citation>
</ref>
<ref id="CR82">
<label>82.</label>
<mixed-citation publication-type="other">MHC, Available from http://www.moh.gov.cn/zhgl/xgxx/fzzsjs/1200304290124.htm.</mixed-citation>
</ref>
<ref id="CR83">
<label>83.</label>
<mixed-citation publication-type="other">MHC, Available from http://www.moh.gov.cn/zhgl/xgxx/fzzsjs/1200306030008.htm.</mixed-citation>
</ref>
<ref id="CR84">
<label>84.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Miiller</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>Optimal vaccination patterns in age-structured populations</article-title>
<source>SIAM J. Appl. Math.</source>
<year>1998</year>
<volume>59</volume>
<fpage>222</fpage>
<pub-id pub-id-type="doi">10.1137/S0036139995293270</pub-id>
</element-citation>
</ref>
<ref id="CR85">
<label>85.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Muldowney</surname>
<given-names>J. S.</given-names>
</name>
</person-group>
<article-title>Compound matrices and ordinary differential equations</article-title>
<source>Rocky Mount. J. Math.</source>
<year>1990</year>
<volume>20</volume>
<fpage>857</fpage>
<pub-id pub-id-type="doi">10.1216/rmjm/1181073047</pub-id>
</element-citation>
</ref>
<ref id="CR86">
<label>86.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Pazy</surname>
<given-names>A.</given-names>
</name>
</person-group>
<source>Semigroups of Linear Operators and Applications to Partial differential Equations</source>
<year>1983</year>
<publisher-loc>Berlin Heidelberg</publisher-loc>
<publisher-name>Springer-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR87">
<label>87.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Perelson</surname>
<given-names>A. S.</given-names>
</name>
<name>
<surname>Kirschner</surname>
<given-names>D. E.</given-names>
</name>
<name>
<surname>De Boer</surname>
<given-names>R. J.</given-names>
</name>
</person-group>
<article-title>Dynamics of HIV infection of CD
<sup>+</sup>
T cells</article-title>
<source>Math. Biosci.</source>
<year>1993</year>
<volume>114</volume>
<fpage>81</fpage>
<pub-id pub-id-type="doi">10.1016/0025-5564(93)90043-A</pub-id>
<pub-id pub-id-type="pmid">8096155</pub-id>
</element-citation>
</ref>
<ref id="CR88">
<label>88.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Culshaw</surname>
<given-names>R. V.</given-names>
</name>
<name>
<surname>Ruan</surname>
<given-names>S.</given-names>
</name>
</person-group>
<article-title>A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay</article-title>
<source>J. Math. Biol.</source>
<year>2003</year>
<volume>46</volume>
<fpage>189</fpage>
<pub-id pub-id-type="doi">10.1007/s00285-002-0191-5</pub-id>
</element-citation>
</ref>
<ref id="CR89">
<label>89.</label>
<mixed-citation publication-type="other">Rao, K. and D. Xu 2003, The talk on CCTV on May 9.</mixed-citation>
</ref>
<ref id="CR90">
<label>90.</label>
<mixed-citation publication-type="other">Riley, S., et al. (2003), Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions, Published online May 23, 2003; 10.1126/science.1086478 (Science Express Reports).</mixed-citation>
</ref>
<ref id="CR91">
<label>91.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Roberts</surname>
<given-names>M. G.</given-names>
</name>
<name>
<surname>Kao</surname>
<given-names>R. R.</given-names>
</name>
</person-group>
<article-title>The dynamics of an infectious disease in a population with birth pulses</article-title>
<source>Math. Biosci.</source>
<year>1998</year>
<volume>149</volume>
<fpage>23</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(97)10016-5</pub-id>
<pub-id pub-id-type="pmid">9610109</pub-id>
</element-citation>
</ref>
<ref id="CR92">
<label>92.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Ross</surname>
<given-names>R.</given-names>
</name>
</person-group>
<source>The prevention of Malaria</source>
<year>1911</year>
<edition>2nd edn</edition>
<publisher-loc>London</publisher-loc>
<publisher-name>Murray</publisher-name>
</element-citation>
</ref>
<ref id="CR93">
<label>93.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ruan</surname>
<given-names>S. G.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>W. D.</given-names>
</name>
</person-group>
<article-title>Dynamic behavior of an epidemic model with a nonlinear incidence rate</article-title>
<source>J. Diff. Eqns.</source>
<year>2003</year>
<volume>18</volume>
<fpage>135</fpage>
<pub-id pub-id-type="doi">10.1016/S0022-0396(02)00089-X</pub-id>
</element-citation>
</ref>
<ref id="CR94">
<label>94.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shulgin</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Stone</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Agur</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Pulse vaccination strategy in the SIR epidemic model</article-title>
<source>Bull. Math. Biol.</source>
<year>1998</year>
<volume>60</volume>
<fpage>1123</fpage>
<pub-id pub-id-type="doi">10.1016/S0092-8240(98)90005-2</pub-id>
<pub-id pub-id-type="pmid">9866452</pub-id>
</element-citation>
</ref>
<ref id="CR95">
<label>95.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Stone</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Shulgin</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Agur</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Theoretical examination of the pulse vaccination policy in the SIR epidemic model</article-title>
<source>Mathl. Comput. Modeling</source>
<year>2000</year>
<volume>31</volume>
<fpage>207</fpage>
<pub-id pub-id-type="doi">10.1016/S0895-7177(00)00040-6</pub-id>
</element-citation>
</ref>
<ref id="CR96">
<label>96.</label>
<mixed-citation publication-type="other">Tang, S. Y., Y. N. Xiao and L. S. Chen, The dynamics of SIS epidemic models with pulse vaccination, to appear.</mixed-citation>
</ref>
<ref id="CR97">
<label>97.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Van den Driessche</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Watmough</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>A simple SIS epidemic model with a backward bifurcation</article-title>
<source>J. Math. Biol.</source>
<year>2000</year>
<volume>40</volume>
<fpage>525</fpage>
<pub-id pub-id-type="doi">10.1007/s002850000032</pub-id>
<pub-id pub-id-type="pmid">10945647</pub-id>
</element-citation>
</ref>
<ref id="CR98">
<label>98.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Venturino</surname>
<given-names>E.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>Epidemics in predator-prey models: Disease in the prey</article-title>
<source>Mathematical population dynamics: Analysis of heterogeneity</source>
<year>1995</year>
<publisher-loc>Canada</publisher-loc>
<publisher-name>Wuerz Publishing</publisher-name>
</element-citation>
</ref>
<ref id="CR99">
<label>99.</label>
<mixed-citation publication-type="other">Wang, F. and Z. E. Ma (2004), Persistence and periodic orbits for SIS model in a polluted environment, to appear in Comput. Math. Appl.</mixed-citation>
</ref>
<ref id="CR100">
<label>100.</label>
<mixed-citation publication-type="other">Wang, F., Z. Ma and Y. M. Shao (2004), A competition model of HIV with recombination effect, to appear on Mathl. Comput. Modelling.</mixed-citation>
</ref>
<ref id="CR101">
<label>101.</label>
<mixed-citation publication-type="other">Wang, F., Z. Ma and Y. M. Shao, Recombination HIV model with time delay, to appear.</mixed-citation>
</ref>
<ref id="CR102">
<label>102.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>W. D.</given-names>
</name>
</person-group>
<article-title>Global Behavior of an SEIRS epidemic model time delays</article-title>
<source>Appl. Math. Lett.</source>
<year>2002</year>
<volume>15</volume>
<fpage>423</fpage>
<pub-id pub-id-type="doi">10.1016/S0893-9659(01)00153-7</pub-id>
</element-citation>
</ref>
<ref id="CR103">
<label>103.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>W. D.</given-names>
</name>
</person-group>
<source>Stability and bifurcation of epidemic mathematical models</source>
<year>2002</year>
<publisher-loc>Xi’an, China</publisher-loc>
<publisher-name>Xi’an Jiaotong University</publisher-name>
</element-citation>
</ref>
<ref id="CR104">
<label>104.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>W. D.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<article-title>Global dynamics of an epidemic model with time delay</article-title>
<source>Nonlinear Analysis: Real Word Applications</source>
<year>2002</year>
<volume>3</volume>
<fpage>365</fpage>
<pub-id pub-id-type="doi">10.1016/S1468-1218(01)00035-9</pub-id>
</element-citation>
</ref>
<ref id="CR105">
<label>105.</label>
<mixed-citation publication-type="other">WHO and CDC, Available from http://www.moh.gov.cn/was40/detail?record=14&channelid=8085 &searchword=%B7%C7%B5%E4%D2%DF%C3%E7.</mixed-citation>
</ref>
<ref id="CR106">
<label>106.</label>
<mixed-citation publication-type="other">WHO, Available from http://www.who.int/csr/sars/country/2003_06_13/en.</mixed-citation>
</ref>
<ref id="CR107">
<label>107.</label>
<mixed-citation publication-type="other">World Health Organization Report (1995).</mixed-citation>
</ref>
<ref id="CR108">
<label>108.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wu</surname>
<given-names>L.-I.</given-names>
</name>
<name>
<surname>Feng</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Homoclinic bifurcation in an SIQR model for childhood diseases</article-title>
<source>J. Diff. Eqnt.</source>
<year>2000</year>
<volume>168</volume>
<fpage>150</fpage>
<pub-id pub-id-type="doi">10.1006/jdeq.2000.3882</pub-id>
</element-citation>
</ref>
<ref id="CR109">
<label>109.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>Y. N.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L. S.</given-names>
</name>
</person-group>
<article-title>On an SIS epidemic model with stage structure</article-title>
<source>J. Sys. Sci. and complexity</source>
<year>2003</year>
<volume>16</volume>
<fpage>275</fpage>
</element-citation>
</ref>
<ref id="CR110">
<label>110.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>Y. N.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L.. S.</given-names>
</name>
</person-group>
<article-title>Analysis of a SIS epidemic model with stage structure and a delay</article-title>
<source>Communications in Nonlinear Sci. and Numer. Simul.</source>
<year>2001</year>
<volume>1</volume>
<fpage>35</fpage>
<pub-id pub-id-type="doi">10.1016/S1007-5704(01)90026-7</pub-id>
</element-citation>
</ref>
<ref id="CR111">
<label>111.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>Y. N.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L.S.</given-names>
</name>
</person-group>
<article-title>Modelling and analysis of a predator-prey model with disease in the prey</article-title>
<source>Math. Biosci.</source>
<year>2001</year>
<volume>170</volume>
<fpage>59</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(01)00049-9</pub-id>
<pub-id pub-id-type="pmid">11259803</pub-id>
</element-citation>
</ref>
<ref id="CR112">
<label>112.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>Y. N.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L. S.</given-names>
</name>
<name>
<surname>ven den Bosch</surname>
<given-names>F.</given-names>
</name>
</person-group>
<article-title>Dynamical behavior for a stage-structured SIR infectious disease model</article-title>
<source>Nonlinear Analysis: Real Word Applications</source>
<year>2002</year>
<volume>3</volume>
<fpage>175</fpage>
<pub-id pub-id-type="doi">10.1016/S1468-1218(01)00021-9</pub-id>
</element-citation>
</ref>
<ref id="CR113">
<label>113.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>Y. N.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L. S.</given-names>
</name>
</person-group>
<article-title>A SIS epidemic model with stage structure and a delay</article-title>
<source>Acta Math. Appl. Sinica, English Series</source>
<year>2002</year>
<volume>18</volume>
<fpage>607</fpage>
<pub-id pub-id-type="doi">10.1007/s102550200063</pub-id>
</element-citation>
</ref>
<ref id="CR114">
<label>114.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yuan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Global stability and Hopf bifurcation of an SIS epidemic model with time delays</article-title>
<source>J. System Sci. Complexity</source>
<year>2001</year>
<volume>14</volume>
<fpage>327</fpage>
</element-citation>
</ref>
<ref id="CR115">
<label>115.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yuan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Study on an epidemic model with time variant delay</article-title>
<source>J. System Sci. Complexity</source>
<year>2002</year>
<volume>14</volume>
<fpage>299</fpage>
</element-citation>
</ref>
<ref id="CR116">
<label>116.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yuan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Han</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Analysis of an SIS epidemiologic model with variable population size and a delay</article-title>
<source>Appl. Math. J. Chinese Univ. Ser.B</source>
<year>2003</year>
<volume>16</volume>
<fpage>9</fpage>
</element-citation>
</ref>
<ref id="CR117">
<label>117.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yuan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Jin</surname>
<given-names>Z.</given-names>
</name>
</person-group>
<article-title>Persistence and periodic solution on nonautonomous SIS model with delays</article-title>
<source>Acta Appl. Math. Sinica, English Series</source>
<year>2003</year>
<volume>19</volume>
<fpage>167</fpage>
<pub-id pub-id-type="doi">10.1007/s10255-003-0093-3</pub-id>
</element-citation>
</ref>
<ref id="CR118">
<label>118.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<article-title>Global dynamics of an SEIR epidemic model with saturating contact rate</article-title>
<source>Math. Biosci.</source>
<year>2003</year>
<volume>185</volume>
<fpage>15</fpage>
<pub-id pub-id-type="doi">10.1016/S0025-5564(03)00087-7</pub-id>
<pub-id pub-id-type="pmid">12900140</pub-id>
</element-citation>
</ref>
<ref id="CR119">
<label>119.</label>
<mixed-citation publication-type="other">Zhang, J. and Z. E. Ma, Global dynamics of an SEIR epidemic model with population dependent incidence, to appear.</mixed-citation>
</ref>
<ref id="CR120">
<label>120.</label>
<mixed-citation publication-type="other">Zhang, J., J. Lou, Z. E. Ma and J. H. Wu (2004), A compartmental model for the analysis of SARS transmission patterns and outbreak control measures in China, to appear in Appl. Math. Computations.</mixed-citation>
</ref>
<ref id="CR121">
<label>121.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Zhou</surname>
<given-names>Y. C.</given-names>
</name>
</person-group>
<source>Epidemic models with age-structure and the infective courses and their asymptotical behavior</source>
<year>1999</year>
<publisher-loc>Xi’an, China</publisher-loc>
<publisher-name>Xi’an Jiaotong University</publisher-name>
</element-citation>
</ref>
<ref id="CR122">
<label>122.</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Zhou</surname>
<given-names>Y. C.</given-names>
</name>
<name>
<surname>Song</surname>
<given-names>B. J.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>Z. E.</given-names>
</name>
</person-group>
<person-group person-group-type="editor">
<name>
<surname>Castillo-Chavez</surname>
<given-names>C.</given-names>
</name>
</person-group>
<article-title>The global stability analysis for emerging and reemerging infectious diseases</article-title>
<source>The IMA volumes in mathematics and its applications</source>
<year>2002</year>
<publisher-loc>New York Berlin Heidelberg</publisher-loc>
<publisher-name>Springer-Verlag</publisher-name>
</element-citation>
</ref>
<ref id="CR123">
<label>123.</label>
<mixed-citation publication-type="other">Zhou, Y. C., Z. E. Ma and F. Brauer (2004), A discrete epidemic model for SARS transmission and control in China, to appear on Mathl. Comput. Modelling.</mixed-citation>
</ref>
<ref id="CR124">
<label>124.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhou</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Lou</surname>
<given-names>M. Z.</given-names>
</name>
<name>
<surname>Lou</surname>
<given-names>J.</given-names>
</name>
</person-group>
<article-title>Study of an type of epidemic model with age stage</article-title>
<source>Chinese J. Engin. Math.</source>
<year>2003</year>
<volume>20</volume>
<fpage>135</fpage>
<pub-id pub-id-type="doi">10.3901/JME.2003.08.135</pub-id>
</element-citation>
</ref>
<ref id="CR125">
<label>125.</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhu</surname>
<given-names>L. Y.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Y. C.</given-names>
</name>
</person-group>
<article-title>Global stability of the positive steady solution of epidemic models with vaccination and age structure</article-title>
<source>J. BioMath.</source>
<year>2003</year>
<volume>18</volume>
<fpage>27</fpage>
</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 000149 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Pmc/Corpus/biblio.hfd -nk 000149 | 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=     PMC:7123007
   |texte=   Basic Knowledge and Developing Tendencies in Epidemic Dynamics
}}

Pour générer des pages wiki

HfdIndexSelect -h $EXPLOR_AREA/Data/Pmc/Corpus/RBID.i   -Sk "pubmed:NONE" \
       | HfdSelect -Kh $EXPLOR_AREA/Data/Pmc/Corpus/biblio.hfd   \
       | NlmPubMed2Wicri -a SrasV1 

Wicri

This area was generated with Dilib version V0.6.33.
Data generation: Tue Apr 28 14:49:16 2020. Site generation: Sat Mar 27 22:06:49 2021