Global stability of a multi-group SEI model

In this paper, a multi-group SEI model with the bilinear incidence and variable susceptibility and infectivity is analyzed. The susceptible individuals are divided into n groups according to their susceptibility, and infected individuals are divided into m   groups according to infectivities. Each group of infected individuals has an exposed period. The basic reproduction number R0R0 is obtained, and globally asymptotic stability of disease-free equilibrium is proved if R0⩽1R0⩽1. If R0>1R0>1, the disease-free equilibrium is unstable and the endemic equilibrium exists and is unique, which is globally asymptotically stable. Finally, some numerical examples are given to illustrate the above analysis.