Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence

In this paper, we introduce a basic reproduction number for a multigroup epidemic model with nonlinear incidence. Then, we establish that global dynamics are completely determined by the basic reproduction number R0. It shows that, the basic reproduction number R0 is a global threshold parameter in the sense that if it is less than or equal to one, the disease free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Finally, a numerical example is also included to illustrate the effectiveness of the proposed result.