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Global stability of multi-group SIR epidemic model with group mixing and human movement
1School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China.
Abstract:
In this paper, an SIR multi-group epidemic model with group mixing and human movement is investigated. The control reproduction number ℜυ is derived and the global dynamics of the model are completely determined by the value of ℜυ. By using the graph-theoretical approach, the results show that the disease-free equilibrium is globally asymptotically stable if ℜυ<1, and the unique endemic equilibrium is globally asymptotically stable if ℜυ>1. Two numerical examples are further presented to testify the validity of the theoretical results.
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