The final size of a SARS epidemic model without quarantine

In this article, we present the continuing work on a SARS model without quarantine by Hsu and Hsieh [Sze-Bi Hsu, Ying-Hen Hsieh, Modeling intervention measures and severity-dependent public response during severe acute respiratory syndrome outbreak, SIAM J. Appl. Math. 66 (2006) 627-647]. An acting basic reproductive number Vf is used to predict the final size of the susceptible population. We find the relation among the final susceptible population size S-infinity the initial susceptible population So, and Vf. If psi > 1, The disease will prevail and the final size of the susceptible, S-infinity, becomes zero; therefore, everyone in the population will be infected eventually. If psi < 1, the disease dies out, and then S-infinity > 0 which means part of the population will never be infected. Also, when S infinity > 0, Scc is increasing with respect to the initial susceptible population So, and decreasing with respect to the acting basic reproductive number Vf. (c) 2006 Elsevier Inc. All rights reserved.