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

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China

Special Issues: Modeling and Complex Dynamics of Populations

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

Citation: Qianqian Cui. Global stability of multi-group SIR epidemic model with group mixing and human movement. Mathematical Biosciences and Engineering, 2019, 16(4): 1798-1814. doi: 10.3934/mbe.2019087

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