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Explicit numerical approximation for an impulsive stochastic age-structured HIV infection model with Markovian switching

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  • Guo, Wenjuan
  • Zhang, Qimin

Abstract

This paper considers an impulsive switching human immunodeficiency virus (HIV) infection model incorporating the mean-reverting Ornstein–Uhlenbeck process. The model involve the virus-to-cell infection and cell-to-cell transmission and has an explicit age-dependent structure. Due to the exact solution of this system cannot be expressed explicitly, it is necessary to give a suitable numerical method to discuss the numerical solution. In this paper, we apply the truncated Euler–Maruyama (EM) method to investigate the explicit numerical approximation for the impulsive stochastic age-structured HIV infection model with Markovian switching. We study the pth moment boundedness of the numerical solution, and the corresponding strong convergence of such algorithm. Numerical simulations are presented to demonstrate the validity of our findings.

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  • 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.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:86-115
    DOI: 10.1016/j.matcom.2020.10.015
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    References listed on IDEAS

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    1. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    2. 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.
    3. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    4. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 684-704.
    5. 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.
    6. Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
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    Cited by:

    1. Qi, Haokun & Meng, Xinzhu, 2021. "Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 700-719.

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