Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size
Identifieur interne : 000E28 ( Main/Exploration ); précédent : 000E27; suivant : 000E29Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size
Auteurs : Supatcha Siriprapaiwan [Thaïlande] ; Elvin J. Moore [Thaïlande] ; Sanoe Koonprasert [Thaïlande]Source :
- Mathematics and Computers in Simulation [ 0378-4754 ] ; 2017.
Abstract
An SEQIJR model of epidemic disease transmission which includes immunization and a varying population size is studied. The model includes immunization of susceptible people (S), quarantine (Q) of exposed people (E), isolation (J) of infectious people (I), a recovered population (R), and variation in population size due to natural births and deaths and deaths of infected people. It is shown analytically that the model has a disease-free equilibrium state which always exists and an endemic equilibrium state which exists if and only if the disease-free state is unstable. A simple formula is obtained for a generalized reproduction number
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DOI: 10.1016/j.matcom.2017.10.006
PubMed: NONE
PubMed Central: 7127447
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size</title><author><name sortKey="Siriprapaiwan, Supatcha" sort="Siriprapaiwan, Supatcha" uniqKey="Siriprapaiwan S" first="Supatcha" last="Siriprapaiwan">Supatcha Siriprapaiwan</name><affiliation wicri:level="1"><nlm:aff id="aff1">Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800</wicri:regionArea><wicri:noRegion>Bangkok 10800</wicri:noRegion></affiliation></author><author><name sortKey="Moore, Elvin J" sort="Moore, Elvin J" uniqKey="Moore E" first="Elvin J." last="Moore">Elvin J. Moore</name><affiliation wicri:level="1"><nlm:aff id="aff1">Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800</wicri:regionArea><wicri:noRegion>Bangkok 10800</wicri:noRegion></affiliation><affiliation wicri:level="1"><nlm:aff id="aff2">Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400</wicri:regionArea><wicri:noRegion>Bangkok 10400</wicri:noRegion></affiliation></author><author><name sortKey="Koonprasert, Sanoe" sort="Koonprasert, Sanoe" uniqKey="Koonprasert S" first="Sanoe" last="Koonprasert">Sanoe Koonprasert</name><affiliation wicri:level="1"><nlm:aff id="aff1">Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800</wicri:regionArea><wicri:noRegion>Bangkok 10800</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmc">7127447</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7127447</idno><idno type="RBID">PMC:7127447</idno><idno type="doi">10.1016/j.matcom.2017.10.006</idno><idno type="pmid">NONE</idno><date when="2017">2017</date><idno type="wicri:Area/Pmc/Corpus">001274</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">001274</idno><idno type="wicri:Area/Pmc/Curation">001274</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">001274</idno><idno type="wicri:Area/Pmc/Checkpoint">000623</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Checkpoint">000623</idno><idno type="wicri:Area/Ncbi/Merge">003E53</idno><idno type="wicri:Area/Ncbi/Curation">003E53</idno><idno type="wicri:Area/Ncbi/Checkpoint">003E53</idno><idno type="wicri:doubleKey">0378-4754:2017:Siriprapaiwan S:generalized:reproduction:numbers</idno><idno type="wicri:Area/Main/Merge">000E30</idno><idno type="wicri:Area/Main/Curation">000E28</idno><idno type="wicri:Area/Main/Exploration">000E28</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size</title><author><name sortKey="Siriprapaiwan, Supatcha" sort="Siriprapaiwan, Supatcha" uniqKey="Siriprapaiwan S" first="Supatcha" last="Siriprapaiwan">Supatcha Siriprapaiwan</name><affiliation wicri:level="1"><nlm:aff id="aff1">Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800</wicri:regionArea><wicri:noRegion>Bangkok 10800</wicri:noRegion></affiliation></author><author><name sortKey="Moore, Elvin J" sort="Moore, Elvin J" uniqKey="Moore E" first="Elvin J." last="Moore">Elvin J. Moore</name><affiliation wicri:level="1"><nlm:aff id="aff1">Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800</wicri:regionArea><wicri:noRegion>Bangkok 10800</wicri:noRegion></affiliation><affiliation wicri:level="1"><nlm:aff id="aff2">Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400</wicri:regionArea><wicri:noRegion>Bangkok 10400</wicri:noRegion></affiliation></author><author><name sortKey="Koonprasert, Sanoe" sort="Koonprasert, Sanoe" uniqKey="Koonprasert S" first="Sanoe" last="Koonprasert">Sanoe Koonprasert</name><affiliation wicri:level="1"><nlm:aff id="aff1">Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand</nlm:aff><country xml:lang="fr">Thaïlande</country><wicri:regionArea>Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800</wicri:regionArea><wicri:noRegion>Bangkok 10800</wicri:noRegion></affiliation></author></analytic><series><title level="j">Mathematics and Computers in Simulation</title><idno type="ISSN">0378-4754</idno><idno type="eISSN">0378-4754</idno><imprint><date when="2017">2017</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>An SEQIJR model of epidemic disease transmission which includes immunization and a varying population size is studied. The model includes immunization of susceptible people (S), quarantine (Q) of exposed people (E), isolation (J) of infectious people (I), a recovered population (R), and variation in population size due to natural births and deaths and deaths of infected people. It is shown analytically that the model has a disease-free equilibrium state which always exists and an endemic equilibrium state which exists if and only if the disease-free state is unstable. A simple formula is obtained for a generalized reproduction number <inline-formula><mml:math id="mml259" display="inline" overflow="scroll" altimg="si259.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> where, for any given initial population, <inline-formula><mml:math id="mml260" display="inline" overflow="scroll" altimg="si260.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> means that the initial population is locally asymptotically stable and <inline-formula><mml:math id="mml261" display="inline" overflow="scroll" altimg="si261.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> means that the initial population is unstable. As special cases, simple formulas are given for the basic reproduction number <inline-formula><mml:math id="mml262" display="inline" overflow="scroll" altimg="si223.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>, a disease-free reproduction number <inline-formula><mml:math id="mml263" display="inline" overflow="scroll" altimg="si159.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and an endemic reproduction number <inline-formula><mml:math id="mml264" display="inline" overflow="scroll" altimg="si227.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. Formulas are derived for the sensitivity indices for variations in model parameters of the disease-free reproduction number <inline-formula><mml:math id="mml265" display="inline" overflow="scroll" altimg="si159.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and for the infected populations in the endemic equilibrium state. A simple formula in terms of the basic reproduction number <inline-formula><mml:math id="mml266" display="inline" overflow="scroll" altimg="si223.gif"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> is derived for the critical immunization level required to prevent the spread of disease in an initially disease-free population. Numerical simulations are carried out using the Matlab program for parameters corresponding to the outbreaks of severe acute respiratory syndrome (SARS) in Beijing, Hong Kong, Canada and Singapore in 2002 and 2003. From the sensitivity analyses for these four regions, the parameters are identified that are the most important for preventing the spread of disease in a disease-free population or for reducing infection in an infected population. The results support the importance of isolating infectious individuals in an epidemic and in maintaining a critical level of immunity in a population to prevent a disease from occurring.</p></div></front><back><div1 type="bibliography"><listBibl><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. 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Brauer</name></author></analytic></biblStruct></listBibl></div1></back></TEI><affiliations><list><country><li>Thaïlande</li></country></list><tree><country name="Thaïlande"><noRegion><name sortKey="Siriprapaiwan, Supatcha" sort="Siriprapaiwan, Supatcha" uniqKey="Siriprapaiwan S" first="Supatcha" last="Siriprapaiwan">Supatcha Siriprapaiwan</name></noRegion><name sortKey="Koonprasert, Sanoe" sort="Koonprasert, Sanoe" uniqKey="Koonprasert S" first="Sanoe" last="Koonprasert">Sanoe Koonprasert</name><name sortKey="Moore, Elvin J" sort="Moore, Elvin J" uniqKey="Moore E" first="Elvin J." last="Moore">Elvin J. Moore</name><name sortKey="Moore, Elvin J" sort="Moore, Elvin J" uniqKey="Moore E" first="Elvin J." last="Moore">Elvin J. Moore</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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