Global stability of multi-group epidemic models with distributed delays

We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0⩽1, then the disease-free equilibrium is globally asymptotically stable; if R0>1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.