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Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility

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  • Junyuan Yang
  • Xiaoyan Wang

Abstract

We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number and some assumptions for the incidence rate.

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  • Junyuan Yang & Xiaoyan Wang, 2018. "Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility," Complexity, Hindawi, vol. 2018, pages 1-15, October.
    • Handle: RePEc:hin:complx:9613807
    DOI: 10.1155/2018/9613807
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    Cited by:

    1. Wenjun Hu & Haiyan Tian & Gang Zhang, 2019. "Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations," Complexity, Hindawi, vol. 2019, pages 1-8, October.

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