The introduction of Lvy noise in stochastic Hepatitis B epidemic model SACVR for comprehending its dynamical behavior and related impacts are focused in this work. For this purpose, the existence, and the uniqueness of the positive solution are proved at first. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Further, convert the proposed Hepatitis B epidemic model to Fractal-fractional Atangana-Baleanu order model and analyzed for the qualitative Fractal-fractional theory. For additional support, ultimately to support the obtained theoretical results, numerical simulations are performed.

本工作重点介绍了在随机乙型肝炎流行模型 SACVR 中引入 Lvy 噪声以了解其动态行为和相关影响。为此，首先证明正解的存在性和唯一性。然后，我们建立一个随机阈值作为该疾病平均灭绝和持续存在的充分条件。此外，将提出的乙型肝炎流行模型转换为分形分数 Atangana-Baleanu 阶模型，并分析定性分形分数理论。对于额外的支持，最终为了支持获得的理论结果，进行了数值模拟。