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

被引：0
作者：
Wang X. [1 ]
Tan Y. [1 ]
Cai Y. [2 ]
Wang K. [3 ]
Wang W. [2 ]
机构：
[1] School of Arts and Science, Shaanxi University of Science and Technology Shaanxi, Xi’an
[2] School of Mathematics and Statistics, Huaiyin Normal University, Huaian
[3] School of Mathematics and Statistics, Southwest University, Chongqing
来源：
Mathematical Biosciences and Engineering | 2021年 / 18卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Asymptotic behavior; Cell-to-cell transmission; HBV infection model; Immune response;
D O I：
10.3934/MBE.2021034
中图分类号：
学科分类号：
摘要：
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 R0, we prove that R0 can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if R0 ≤ 1, 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 R0 > 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. © 2021 the Author(s),
引用
收藏
页码：616 / 642
页数：26
相关论文
共 36 条
  • [1] Nowak M., May R. M., Population dynamics of immune responses to persistent viruses, Science, 272, pp. 74-79, (1996)
  • [2] Arnaout R. A., Nowak M. A., Competitive coexistence in antiviral immunity, J. Theor. Biol, 204, pp. 431-441, (2000)
  • [3] Culshaw R. V., Ruan S., Spiteri R. J., Optimal HIV treatment by maximising immune response, J. Math. Biol, 48, pp. 545-562, (2004)
  • [4] Bertacchi D., Zucca F., Foresti S., Mangioni D., Gori A., Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach, Math. Med. Biol, 32, pp. 383-403, (2015)
  • [5] Neumann A. U., Hepatitis B viral kinetics: A dynamic puzzle still to be resolved, Hepatology, 42, pp. 249-254, (2005)
  • [6] Nowak M., May R. M., Virus Dynamics: Mathematical Principles of Immunology and Virology: Mathematical Principles of Immunology and Virology, (2000)
  • [7] Li J., Men K., Yang Y., Li D., Dynamical analysis on a chronic hepatitis C virus infection model with immune response, J. Theor. Biol, 365, pp. 337-346, (2015)
  • [8] Li M., Zu J., The review of differential equation models of HBV infection dynamics, J. Virol. Meth, 266, pp. 103-113, (2019)
  • [9] Mojaver A., Kheiri H., Dynamical analysis of a class of hepatitis C virus infection models with application of optimal control, Inter. J. Biomath, 9, (2016)
  • [10] Mothes W., Sherer N. M., Jin J., Zhong P., Virus cell-to-cell transmission, J. Virol, 84, pp. 8360-8368, (2010)
1234