Qualitative study of a quarantine/isolation model with multiple disease stages
Identifieur interne : 003F80 ( Ncbi/Curation ); précédent : 003F79; suivant : 003F81Qualitative study of a quarantine/isolation model with multiple disease stages
Auteurs : Mohammad A. Safi ; Abba B. GumelSource :
- Applied Mathematics and Computation [ 0096-3003 ] ; 2011.
Abstract
Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique endemic equilibrium when the threshold quantity exceeds unity. The endemic equilibrium is shown to be locally and globally-asymptotically stable for special cases. Numerical simulations, using data related to the 2003 SARS outbreaks, show that the cumulative number of disease-related mortality increases with increasing number of disease stages. Furthermore, the cumulative number of new cases is higher if the asymptomatic period is distributed such that most of the period is spent in the early stages of the asymptomatic compartments in comparison to the cases where the average time period is equally distributed among the associated stages or if most of the time period is spent in the later (final) stages of the asymptomatic compartments. Finally, it is shown that distributing the average sojourn time in the infectious (asymptomatic) classes equally or unequally does not effect the cumulative number of new cases.
Url:
DOI: 10.1016/j.amc.2011.07.007
PubMed: NONE
PubMed Central: 7112307
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Qualitative study of a quarantine/isolation model with multiple disease stages</title><author><name sortKey="Safi, Mohammad A" sort="Safi, Mohammad A" uniqKey="Safi M" first="Mohammad A." last="Safi">Mohammad A. Safi</name></author><author><name sortKey="Gumel, Abba B" sort="Gumel, Abba B" uniqKey="Gumel A" first="Abba B." last="Gumel">Abba B. 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Safi</name></author><author><name sortKey="Gumel, Abba B" sort="Gumel, Abba B" uniqKey="Gumel A" first="Abba B." last="Gumel">Abba B. Gumel</name></author></analytic><series><title level="j">Applied Mathematics and Computation</title><idno type="ISSN">0096-3003</idno><idno type="eISSN">0096-3003</idno><imprint><date when="2011">2011</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique endemic equilibrium when the threshold quantity exceeds unity. The endemic equilibrium is shown to be locally and globally-asymptotically stable for special cases. Numerical simulations, using data related to the 2003 SARS outbreaks, show that the cumulative number of disease-related mortality increases with increasing number of disease stages. Furthermore, the cumulative number of new cases is higher if the asymptomatic period is distributed such that most of the period is spent in the early stages of the asymptomatic compartments in comparison to the cases where the average time period is equally distributed among the associated stages or if most of the time period is spent in the later (final) stages of the asymptomatic compartments. Finally, it is shown that distributing the average sojourn time in the infectious (asymptomatic) classes equally or unequally does not effect the cumulative number of new cases.</p></div></front><back><div1 type="bibliography"><listBibl><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="Chowell, G" uniqKey="Chowell G">G. 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