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A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay

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  • Sun, Hongquan
  • Li, Jin

Abstract

In this paper, we propose a numerical method for a diffusive virus dynamics model with general incidence function, cell-to-cell transmission and time delay. We justify the wellposedness of the numerical model, and prove that the proposed method preserves the global stability of equilibria by constructing suitable discrete Lyapunov functionals with no constraints on the time and space step sizes. we perform numerical simulation to verify our theoretic results. Epidemiologically, we deduce that the spatial heterogeneity of transmission rate can enlarge the risk of disease outbreaks, and the larger time delay is conductive to cure diseases.

Suggested Citation

  • Sun, Hongquan & Li, Jin, 2020. "A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119319417
    DOI: 10.1016/j.physa.2019.123477
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    References listed on IDEAS

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    1. David D. Ho & Avidan U. Neumann & Alan S. Perelson & Wen Chen & John M. Leonard & Martin Markowitz, 1995. "Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection," Working Papers 95-01-002, Santa Fe Institute.
    2. 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.
    3. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
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