School of Computer Science, Shaanxi Normal University, Xi'an 710119, China.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China.
Math Biosci Eng. 2022 May 23;19(8):7570-7585. doi: 10.3934/mbe.2022356.
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.
乙型肝炎是一种损害肝脏的疾病，其控制已成为一个亟待解决的公共卫生问题。在本文中，我们分析和数值研究了一个新的具有抗病毒治疗和细胞毒性 T 淋巴细胞（CTL）免疫反应的乙型肝炎病毒（HBV）感染模型的动力学。通过使用随机微分方程理论，构建合适的李雅普诺夫函数并应用伊藤公式，我们证明了随机 HBV 模型的无病平衡点在大范围内是随机渐近稳定的，这表明 HBV 感染将以概率 1 被根除。此外，还研究了相应确定性 HBV 模型地方病平衡点附近随机模型全局正解的渐近行为。通过使用米尔斯坦方法，我们提供了数值模拟来支持分析结果，结果表明，较小的噪声不会改变动态行为，而较大的噪声会导致感染的消失。此外，在一定程度上，抑制病毒产生的效果比阻止新感染的效果更为显著，两种治疗方法的结合可能是减少 HBV 感染和游离病毒浓度的更好方法。
