Abstract：
Hepatitis B virus (HBV) infection is a global public health problem and there are 257 million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.
摘要：
乙型肝炎病毒（HBV）感染是一个全球性的公共卫生问题，全世界有2.57亿人患有慢性HBV感染。在本文中,我们研究了具有媒体报道和饱和发病率的随机HBV传播模型的动力学。首先,证明了随机模型正解的存在性和唯一性。然后获得HBV感染消失的条件，这意味着，媒体的报道有助于控制疾病的传播和噪声强度对急性和慢性HBV感染起到了关键的作用。此外，我们验证了该系统在一定条件下具有独特的平稳分布，从生物学的角度来看，这种疾病将占上风。进行了数值模拟，以直观地说明我们的理论结果。作为一个案例研究，我们将我们的模型拟合到2005年至2021年中国大陆可用的乙型肝炎数据。
