# American Institute of Mathematical Sciences

2006, 3(3): 485-512. doi: 10.3934/mbe.2006.3.485

## An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

 1 Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada 2 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada 3 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada

Received  September 2005 Revised  January 2006 Published  May 2006

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some 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. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number ($\R_{v}$). If $\R_{v}\le 1$, the disease will be eliminated from the community; whereas an epidemic occurs if $\R_{v}>1$. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming $\R=4$). Numerical simulations are used to explore the severity of outbreaks when $\R_{v}>1$.
Citation: Abba B. Gumel, C. Connell McCluskey, James Watmough. An sveir model for assessing potential impact of an imperfect anti-SARS vaccine. Mathematical Biosciences & Engineering, 2006, 3 (3) : 485-512. doi: 10.3934/mbe.2006.3.485
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