AN EPIDEMIC MODEL STRUCTURED BY HOST IMMUNITY

Abstract

In this paper we introduce a physiologically structured SIR epidemic model where the individuals are distributed according to their immune status. An individual immune status is assumed to increase during the infectious period and remain unchanged after the recovery. Recovered individuals can become reinfected at a rate which is a decreasing function of their immune status. We find that the possibility of reinfection of recovered individuals results in subthreshold endemic equilibria. The differential immunity of the infectious individuals leads to multiple nontrivial equilibria in the superthreshold case. We present an example that has exactly three nontrivial equilibria. We also analyze the local stability of equilibria.