An sveir model for assessing potential impact of an imperfect anti-SARS vaccine
The control of severe acute respiratory syndrome (SARS), a fatalcontagious viral disease that spread to over 32 countries in 2003,was based on quarantine of latently infected individuals and isolation ofindividuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials ofsome ca...
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AIMS Press
2006-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.485 |
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| author | Abba B. Gumel C. Connell McCluskey James Watmough |
| author_facet | Abba B. Gumel C. Connell McCluskey James Watmough |
| author_sort | Abba B. Gumel |
| collection | DOAJ |
| description | The control of severe acute respiratory syndrome (SARS), a fatalcontagious viral disease that spread to over 32 countries in 2003,was based on quarantine of latently infected individuals and isolation ofindividuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials ofsome candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine,assumed to be imperfect, in curtailing future outbreaks. Arelatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamicsof the model are determined by a certain thresholdquantity known as the control reproduction number ($\R_{v}$). If$\R_{v}\le 1$, the disease will be eliminated from the community; whereasan epidemic occurs if $\R_{v}>1$. This study further shows that animperfect SARS vaccine with infection-blocking efficacy is alwaysbeneficial in reducing disease spread within the community, althoughits overall impact increases with increasing efficacy and coverage.In particular, it is shown that thefraction of individuals vaccinated at steady-state and vaccineefficacy play equal roles in reducing disease burden, and thevaccine must have efficacy of at least 75% to lead to effectivecontrol of SARS (assuming $\R=4$). Numerical simulations are used to explore theseverity of outbreaks when $\R_{v}>1$. |
| format | Article |
| id | doaj-art-a2962cf48d8942cfa37a5337ad51af50 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a2962cf48d8942cfa37a5337ad51af502025-01-24T01:51:49ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-04-013348551210.3934/mbe.2006.3.485An sveir model for assessing potential impact of an imperfect anti-SARS vaccineAbba B. Gumel0C. Connell McCluskey1James Watmough2Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2The control of severe acute respiratory syndrome (SARS), a fatalcontagious viral disease that spread to over 32 countries in 2003,was based on quarantine of latently infected individuals and isolation ofindividuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials ofsome candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine,assumed to be imperfect, in curtailing future outbreaks. Arelatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamicsof the model are determined by a certain thresholdquantity known as the control reproduction number ($\R_{v}$). If$\R_{v}\le 1$, the disease will be eliminated from the community; whereasan epidemic occurs if $\R_{v}>1$. This study further shows that animperfect SARS vaccine with infection-blocking efficacy is alwaysbeneficial in reducing disease spread within the community, althoughits overall impact increases with increasing efficacy and coverage.In particular, it is shown that thefraction of individuals vaccinated at steady-state and vaccineefficacy play equal roles in reducing disease burden, and thevaccine must have efficacy of at least 75% to lead to effectivecontrol of SARS (assuming $\R=4$). Numerical simulations are used to explore theseverity of outbreaks when $\R_{v}>1$.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.485severe acuterespiratory syndrome (sars)disease transmission modelcontrol reproduction number.vaccinationepidemiology |
| spellingShingle | Abba B. Gumel C. Connell McCluskey James Watmough An sveir model for assessing potential impact of an imperfect anti-SARS vaccine Mathematical Biosciences and Engineering severe acuterespiratory syndrome (sars) disease transmission model control reproduction number. vaccination epidemiology |
| title | An sveir model for assessing potential impact of an imperfect anti-SARS vaccine |
| title_full | An sveir model for assessing potential impact of an imperfect anti-SARS vaccine |
| title_fullStr | An sveir model for assessing potential impact of an imperfect anti-SARS vaccine |
| title_full_unstemmed | An sveir model for assessing potential impact of an imperfect anti-SARS vaccine |
| title_short | An sveir model for assessing potential impact of an imperfect anti-SARS vaccine |
| title_sort | sveir model for assessing potential impact of an imperfect anti sars vaccine |
| topic | severe acuterespiratory syndrome (sars) disease transmission model control reproduction number. vaccination epidemiology |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.485 |
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