Din Anwarud, Li Yongjin, Yusuf Abdullahi, Liu Jinping, Aly Ayman A
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China.
Department of Computer Engineering, Biruni University, Istanbul, Turkey.
Eur Phys J Spec Top. 2022;231(10):1859-1873. doi: 10.1140/epjs/s11734-022-00453-5. Epub 2022 Feb 4.
This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter , followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have . For the case , adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.
本文旨在通过一种新颖的方法，纳入信息干预和随机扰动的影响，来分析一个SIR型乙肝流行随机模型的动力学行为。首先，我们证明了解的正性和全局存在性。随后，我们推导出随机阈值参数，接着得出这个数值决定乙肝在人群中传播的结论。通过增加噪声强度，我们得到小于1的结果，这意味着最终乙肝将消失。而当把噪声强度降低到足够水平时，我们得到。对于的情况，得到了关于平稳分布存在的充分结果，表明乙肝的流行情况。本研究还涉及推导该流行病持续存在的必要条件。最后，通过模拟绘制出主要的理论解。对理论和数值结果的讨论表明，利用随机扰动和信息干预对该综合征的动态有显著影响。此外，由于大多数社区相互作用，且疾病传播速率受此因素影响，我们提出了一个随机乙肝模型的新的变阶分数网络。随后，本研究将为理解全球范围内与SIR随机和变阶分数网络相关的案例研究提供坚实的理论基础。
