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Numerical analysis of a nonlinear age-structured HBV model with saturated incidence and spatial diffusion

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  • Li, Wenli
  • Liu, Xing
  • Lang, Yanhua

Abstract

In this paper, the numerical properties of a nonlinear age-structured hepatitis B virus model with saturated incidence and spatial diffusion are studied. Applying linearly implicit Euler method in time integration, a numerical scheme which can preserve the biological meanings is constructed. The convergence of the numerical solution in finite time is explored. In stability analysis, a threshold is proposed, which is called numerical basic reproduction number and denoted by R0h. It is proved that the numerical solution is locally asymptotically stable at the disease-free equilibrium when R0h<1. Moreover, it is proved the numerical basic reproduction number converges to the exact basic reproduction number of the model with first order accuracy. Furthermore, it is shown that a numerical space independent equilibrium exists and is asymptotically stable if R0h>1, which implies the threshold stability of the model can be preserved by numerical solution proposed. Eventually, our conclusions are tested through numerical experiments.

Suggested Citation

  • Li, Wenli & Liu, Xing & Lang, Yanhua, 2024. "Numerical analysis of a nonlinear age-structured HBV model with saturated incidence and spatial diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 250-266.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:250-266
    DOI: 10.1016/j.matcom.2024.05.022
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    References listed on IDEAS

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    1. Cao, Shuxing & Chen, Zhijie & Yang, Zhanwen, 2023. "Numerical representations of global epidemic threshold for nonlinear infection-age SIR models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 115-132.
    2. Guo, Wenjuan & Zhang, Qimin, 2021. "Explicit numerical approximation for an impulsive stochastic age-structured HIV infection model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 86-115.
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