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Asymptotic profiles of a nonlocal dispersal SIR epidemic model with treat-age in a heterogeneous environment

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  • Bentout, Soufiane
  • Djilali, Salih

Abstract

Infectious diseases have a significant impact on human life, and additional efforts are required to contain them. Treatment measure is very helpful to contain the epidemic and protect infected persons from disease-related mortality. Therefore, we consider a SIR epidemic model with nonlocal diffusion modeled by a convolution operator and treat-age effect. We show the well-posedness of the solution to the problem that is existence, uniqueness and positivity, and boundedness. Next, we determine the corresponding basic reproduction number R0 that depends on the structure of studied bounded domain Ω∈RN, and we show its threshold role in determining the asymptotic profiles of the solution. Moreover, it is proved that the solution map has a global compact attractor. Indeed, for R0<1, there exist a Lipschitz functions Sp such that (Sp,0,0) is globally stable, which is related to the extinction scenario of the epidemic. However, for R0>1, we show the solution map is uniformly persistent and there exists a unique endemic steady state denoted (S∗,I∗,T∗) that is globally stable. The influence of the treat-age on the spatiotemporal and threshold profiles is discussed through the research.

Suggested Citation

  • Bentout, Soufiane & Djilali, Salih, 2023. "Asymptotic profiles of a nonlocal dispersal SIR epidemic model with treat-age in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 926-956.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:926-956
    DOI: 10.1016/j.matcom.2022.07.020
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    References listed on IDEAS

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    1. Yang, Junyuan & Wang, Xiaoyan, 2019. "Dynamics and asymptotical profiles of an age-structured viral infection model with spatial diffusion," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 236-254.
    2. Mohammed AL-Smadi & Omar Abu Arqub & Ahmad El-Ajou, 2014. "A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, March.
    3. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
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