Stability analysis of a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure

In this paper, we focus on a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure, in which the effects of time delay and population exchange between groups are considered. By using a Lyapunov functional approach, we establish that the global stability of the model is completely determined by a threshold parameter R˜0, that is, the disease-free equilibrium of the model is globally asymptotically stable if R˜0≤1, while an endemic equilibrium of the model is such if R˜0>1. Moreover, in the analysis, we offer new techniques to prove the permanence and the existence of the endemic equilibrium of delayed nonlinear multi-group epidemic models. This result shows that the incidence delay and the migration delay do not alter the quality of the disease dynamics.