Global stability of multi-group SIR epidemic model with group mixing and human movement

In this paper, an SIR multi-group epidemic model with group mixing and human movement is investigated. The control reproduction number R-v is derived and the global dynamics of the model are completely determined by the value of R-v. By using the graph-theoretical approach, the results show that the disease-free equilibrium is globally asymptotically stable if R-v < 1, and the unique endemic equilibrium is globally asymptotically stable if R-v > 1. Two numerical examples are further presented to testify the validity of the theoretical results.