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Discretization and dynamic consistency of a delayed and diffusive viral infection model

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  • Geng, Yan
  • Xu, Jinhu
  • Hou, Jiangyong

Abstract

A diffusive and delayed viral infection model with nonlinear incidence has been studied, and the global dynamical behaviors of the original model is investigated by constructing Lyapunov functionals. Furthermore, the analysis is carried out for the discrete model which is obtained by applying the nonstandard finite difference (NSFD) scheme to the original continuous model. The global stability for the corresponding equilibria is investigated by constructing discrete Lyapunov functionals as well as the positivity and boundedness of solutions of the corresponding continuous model. The results imply that the discretization scheme can efficiently preserves the qualitative properties of solutions for the original continuous model. Numerical experiments are carried out to support the theoretical results.

Suggested Citation

  • Geng, Yan & Xu, Jinhu & Hou, Jiangyong, 2018. "Discretization and dynamic consistency of a delayed and diffusive viral infection model," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 282-295.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:282-295
    DOI: 10.1016/j.amc.2017.08.041
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    References listed on IDEAS

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    1. Wang, Tianlei & Hu, Zhixing & Liao, Fucheng & Ma, Wanbiao, 2013. "Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 13-22.
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    Cited by:

    1. Elaiw, Ahmed M. & Alshaikh, Matuka A., 2020. "Global stability of discrete pathogen infection model with humoral immunity and cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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