Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure

In this paper, we formulate and study a multi-group SIS epidemic model with time-delays, nonlinear incidence rates and patch structure. Two types of delays are incorporated to concern the time-delay of infection and that for population exchange among different groups. Taking into account both of the effects of cross-region infection and the population exchange, we de fine the basic reproduction number R-0 by the spectral radius of the next generation matrix and prove that it is a threshold value, which determines the global stability of each equilibrium of the model. That is, it is shown that if R-0 <= 1, the disease-free equilibrium is globally asymptotically stable, while if R-0 > 1, the system is permanent, an endemic equilibrium exists and it is globally asymptotically stable. These global stability results are achieved by constructing Lyapunov functionals and applying LaSalle's invariance principle to a reduced system. Numerical simulation is performed to support our theoretical results. (C) 2015 All rights reserved.