Dynamics of a stochastic HBV infection model with drug therapy and immune response

Yiping Tan; Yongli Cai; Zhihang Peng; Kaifa Wang; Ruoxia Yao; Weiming Wang; Yiping Tan; Yongli Cai; Zhihang Peng; Kaifa Wang; Ruoxia Yao; Weiming Wang

doi:10.3934/mbe.2022356

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 7570-7585. doi: 10.3934/mbe.2022356

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Dynamics of a stochastic HBV infection model with drug therapy and immune response

1.
School of Computer Science, Shaanxi Normal University, Xi'an 710119, China
2.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China
3.
Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing 211166, China
4.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Academic Editor: Grzegorz A. Rempala

Received: 01 March 2022 Revised: 24 April 2022 Accepted: 12 May 2022 Published: 23 May 2022

Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.
- stochastic HBV infection model,
- drug therapy,
- immune response,
- cure rate,
- extinction
Citation: Yiping Tan, Yongli Cai, Zhihang Peng, Kaifa Wang, Ruoxia Yao, Weiming Wang. Dynamics of a stochastic HBV infection model with drug therapy and immune response[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 7570-7585. doi: 10.3934/mbe.2022356

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Abstract

Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.

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