School of Arts and Science, Shaanxi University of Science and Technology Shaanxi, Xi'an 710021, China.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China.
Math Biosci Eng. 2020 Dec 15;18(1):616-642. doi: 10.3934/mbe.2021034.
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.
在本文中，考虑到外泌体的作用已被证实，以及在宿主内必然存在的随机性，我们从确定性框架建立了一个具有细胞间传播和 CTL 免疫反应的乙型肝炎病毒 (HBV) 模型，并将其转化为随机微分方程 (SDE)。通过引入繁殖数 $ R_0 $，我们证明了 $ R_0 $ 可以用来控制 SDE HBV 模型的随机动力学。在某些假设下，如果 $ R_{0}\leq1 $，SDE 模型的解总是围绕确定性模型的无感染平衡点波动，这表明 HBV 最终将几乎肯定消失；如果 $ R_{0} > 1 $，在额外条件下，SDE 模型的解围绕相应确定性模型的地方病平衡点波动，这导致 HBV 的随机持续存在，其概率为 1。最有趣的发现之一是，波动幅度与白噪声的强度呈正相关，这可以为我们提供一些有用的控制策略来调节 HBV 感染动力学。
