Global stability of a multi-group model with vaccination age, distributed delay and random perturbation.

A multi-group epidemic model with distributed delay and vaccination age has been formulated and studied. Mathematical analysis shows that the global dynamics of the model is determined by the basic reproduction number R0: the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1, and the endemic equilibrium is globally asymptotically stable if R0 > 1. Lyapunov functionals are constructed by the non-negative matrix theory and a novel grouping technique to establish the global stability. The stochastic perturbation of the model is studied and it is proved that the endemic equilibrium of the stochastic model is stochastically asymptotically stable in the large under certain conditions.