The final size of a SARS epidemic model without quarantine

Hsu, Sze-Bi; Roeger, Lih-Ing W.

Abstract 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 S 0 , 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 S 0 , and decreasing with respect to the acting basic reproductive number ψ.