Global stability of an age-structured sir epidemic model with pulse vaccination strategy

Abstract

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age (duration since infection). The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infection-free situation if the impulsive period T and proportion p satisfy R0(p, T) < 1. Optimal problem is discussed: Pulse vaccination strategy with minimal costs at given R0(p, T) < 1.