Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission

The dynamics of multi-group SEIR epidemic models with distributed and infinite delay and nonlinear transmission are investigated. We derive the basic reproduction number R0R0 and establish that the global dynamics are completely determined by the values of R0R0: if R0≤1R0≤1, then the disease-free equilibrium is globally asymptotically stable; if R0>1R0>1, then there exists a unique endemic equilibrium which is globally asymptotically stable. Our results contain those for single-group SEIR models with distributed and infinite delays. In the proof of global stability of the endemic equilibrium, we exploit a graph-theoretical approach to the method of Lyapunov functionals. The biological significance of the results is also discussed.