Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response

Xiaoqin Wang; Yiping Tan; Yongli Cai; Kaifa Wang; Weiming Wang; Xiaoqin Wang; Yiping Tan; Yongli Cai; Kaifa Wang; Weiming Wang

doi:10.3934/mbe.2021034

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 616-642. doi: 10.3934/mbe.2021034

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Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response

1.
School of Arts and Science, Shaanxi University of Science and Technology Shaanxi, Xi'an 710021, China
2.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China
3.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received: 31 July 2020 Accepted: 10 December 2020 Published: 15 December 2020

In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $ R_0 $, we prove that $ R_0 $ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $ R_{0}\leq1 $, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $ R_{0} > 1 $, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.
- HBV infection model,
- immune response,
- cell-to-cell transmission,
- asymptotic behavior
Citation: Xiaoqin Wang, Yiping Tan, Yongli Cai, Kaifa Wang, Weiming Wang. Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 616-642. doi: 10.3934/mbe.2021034

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Abstract

In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $ R_0 $, we prove that $ R_0 $ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $ R_{0}\leq1 $, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $ R_{0} > 1 $, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.

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