Stability analysis of an age-structured epidemic model with vaccination and standard incidence rate

Abstract

Age structure of the host population is a crucial factor in the transmission and control of infectious diseases, since the risk from an infection increases along with age, different age groups interact heterogeneously, vaccination programs focus on specific age groups, and epidemiological data are reported according to ages. In this paper we consider an age-structured epidemic model of the susceptible–exposed–infectious–recovered (SEIR) type with vaccination and standard incidence rate. After establishing the well-posedness of the initial–boundary value problem, we study the existence and stability of the disease-free and endemic steady states based on the basic reproduction number R0. It is shown that the disease-free steady state is globally asymptotically stable if R0<1, the endemic steady state is unique if R0<1 and is locally asymptotically stable under some additional conditions. Some numerical simulations are presented to illustrate the theoretical results.