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Analysis of a general multi-group reaction–diffusion epidemic model with nonlinear incidence and temporary acquired immunity

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  • Luo, Yantao
  • Zhang, Long
  • Teng, Zhidong
  • Zheng, Tingting

Abstract

Considering the individual differences, spatial environment and the temporary acquired immunity, a general multi-group reaction–diffusion epidemic model with nonlinear incidence and temporary acquired immunity is proposed in this paper. The well-posedness of the solution including the existence of global solutions and the ultimate boundedness of the solutions are obtained, and then we define the basic reproduction number R0. Further, the threshold dynamics of the disease are obtained in terms of R0. Moreover, by constructing suitable Lyapunov functions, we obtain the endemic steady state is globally asymptotically stable in homogeneous space and heterogeneous case when R0>1. Based on theoretical analysis, we conclude that the existence of immunity loss rate and the difference of diffusion rate may bring great difficulties to control the disease. Finally, we find the spatial heterogeneity cannot always enhance the infectious risk of the disease and simply increasing the diffusion coefficient cannot effectively control the spread of the disease via some numerical simulations.

Suggested Citation

  • Luo, Yantao & Zhang, Long & Teng, Zhidong & Zheng, Tingting, 2021. "Analysis of a general multi-group reaction–diffusion epidemic model with nonlinear incidence and temporary acquired immunity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 428-455.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:428-455
    DOI: 10.1016/j.matcom.2020.11.002
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    References listed on IDEAS

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    1. Wang, Jinliang & Wang, Jing & Kuniya, Toshikazu, 2019. "Analysis of an age-structured multi-group heroin epidemic model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 78-100.
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    Cited by:

    1. Zhu, Linhe & Zheng, Wenxin & Shen, Shuling, 2023. "Dynamical analysis of a SI epidemic-like propagation model with non-smooth control," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Xinggui Li & Xinsong Yang, 2023. "Global Stabilization of Delayed Feedback Financial System Involved in Advertisement under Impulsive Disturbance," Mathematics, MDPI, vol. 11(9), pages 1-12, April.

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