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” ψ is used to predict the final size of the susceptible population. We find the relation among the final susceptible population size S∞, the initial susceptible population S0, and ψ. If ψ>1, the disease will prevail and the final size of the susceptible, S∞, becomes zero; therefore, everyone in the population will be infected eventually. If ψ<1, the disease dies out, and then S∞>0 which means part of the population will never be infected. Also, when S∞>0, S∞ is increasing with respect to the initial susceptible population S0, and decreasing with respect to the acting basic reproductive number ψ.