An sveir model for assessing potential impact of an imperfect anti-SARS vaccine - Abba B. Gumel; C. Connell McCluskey; James Watmough (Mathematical Biosciences and Engineering)
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 $\R_{v}>1$.