Global stability of an epidemic model with nonlinear incidence rate and differential infectivity

Abstract

This paper considers an SI 1 I 2 R epidemic model that incorporates two classes of infectious individuals with differential infectivity, and the incidence rate is nonlinear. The basic reproduction number R 0 is found. If R 0⩽1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out eventually. If R 0>1, a unique endemic equilibrium is locally asymptotically stable for general assumption. For a special case the global stability of the endemic equilibrium is proved.