Global stability of epidemiological models with group mixing and nonlinear incidence rates

For a multigroup SEIR epidemiological model with nonlinear incidence rates, the basic reproduction number is identified. It is shown that, under certain group mixing patterns and nonlinearity and/or nonsmoothness in the incidence of infection, the basic reproduction number is a global threshold parameter in the sense that the disease free equilibrium is globally stable if the basic reproduction number is less than one and the endemic equilibrium is globally stable if the basic reproduction number is greater than one.