Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE.
Math Biosci Eng. 2021 Jun 10;18(5):5194-5220. doi: 10.3934/mbe.2021264.
Considering the environmental factors and uncertainties, we propose, in this paper, a higher-order stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases.
考虑到环境因素和不确定性，我们提出了一个具有免疫系统的乙型肝炎病毒（HBV）感染动力学的高阶随机摄动时滞微分模型。研究了系统正解遍历平稳分布的存在性和唯一性，其中解围绕确定性模型的地方病平衡点波动，导致疾病的随机持久性。在某些条件下，可以获得无感染的情况，疾病以概率 1 指数衰减。通过使用 Milstein 方案进行了一些数值模拟，以显示所得到的结果的有效性。白噪声的强度在传染病的治疗中起着重要作用。
