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

This paper considers an SI1I2R epidemic model that incorporates two classes of infectious individuals with differential infectivity, and the incidence rate is nonlinear. The basic reproduction number R0 is found. If R0⩽1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out eventually. If R0>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.