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A reaction–diffusion Susceptible–Vaccinated–Infected–Recovered model in a spatially heterogeneous environment with Dirichlet boundary condition

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  • Wang, Jinliang
  • Zhang, Ran
  • Kuniya, Toshikazu

Abstract

In this paper, we study a Susceptible–Vaccinated–Infected–Recovered (SVIR) epidemic model in a spatially heterogeneous environment under the Dirichlet boundary condition. We define the basic reproduction number ℜ0 by the spectral radius of the next generation operator, and show that it is a threshold parameter. The disease extinction and persistence in the case of a bounded domain are considered. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if ℜ0<1; the system is uniformly persistent and an endemic equilibrium exists if ℜ0>1. To verify our theoretical results, we perform some numerical simulations, using the Fredholm discretization method to identify ℜ0.

Suggested Citation

  • Wang, Jinliang & Zhang, Ran & Kuniya, Toshikazu, 2021. "A reaction–diffusion Susceptible–Vaccinated–Infected–Recovered model in a spatially heterogeneous environment with Dirichlet boundary condition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 848-865.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:848-865
    DOI: 10.1016/j.matcom.2021.06.020
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    References listed on IDEAS

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    1. Bai, Zhenguo & Wu, Shi-Liang, 2015. "Traveling waves in a delayed SIR epidemic model with nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 221-232.
    2. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    3. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C), pages 1-1.
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    Cited by:

    1. Wang, Jianpeng & Wang, Kai & Zheng, Tingting & Zhou, Pan & Teng, Zhidong, 2024. "Qualitative analysis on a reaction–diffusion SIS epidemic model with nonlinear incidence and Dirichlet boundary," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    3. Martin Kröger & Reinhard Schlickeiser, 2024. "On the Analytical Solution of the SIRV-Model for the Temporal Evolution of Epidemics for General Time-Dependent Recovery, Infection and Vaccination Rates," Mathematics, MDPI, vol. 12(2), pages 1-19, January.

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