论文标题
SIS流行病学模型具有隔离策略，随机传播和莱维干扰的新结果
New results on the asymptotic behavior of an SIS epidemiological model with quarantine strategy, stochastic transmission, and Lévy disturbance
论文作者
论文摘要
传染病的传播是我们当代世界中的主要挑战，尤其是在最近的2019年冠状病毒病（Covid-19）爆发之后。隔离策略是通过极大地减少感染和易感人群接触的可能性来控制流行病的重要措施之一。在这项研究中，我们分析了隔离期间各种随机障碍对流行动力学的影响。为此，我们提出了一个SIQS流行模型，该模型结合了随机传播和Lévy噪声，以模拟小型和巨大的扰动。在适当的条件下，证明了一些有趣的渐近特性，即：疾病的均值，平均值和灭绝。理论结果表明，扰动模型的动力学是由与随机噪声密切相关的参数确定的。我们的工作改善了数学流行病学领域的许多现有研究，并提供了预测和分析流行病的动态行为的新技术。
The spread of infectious diseases is a major challenge in our contemporary world, especially after the recent outbreak of Coronavirus disease 2019 (COVID-19). The quarantine strategy is one of the important intervention measures to control the spread of an epidemic by greatly minimizing the likelihood of contact between infected and susceptible individuals. In this study, we analyze the impact of various stochastic disturbances on the epidemic dynamics during the quarantine period. For this purpose, we present an SIQS epidemic model that incorporates the stochastic transmission and the Lévy noise in order to simulate both small and massive perturbations. Under appropriate conditions, some interesting asymptotic properties are proved, namely: ergodicity, persistence in the mean, and extinction of the disease. The theoretical results show that the dynamics of the perturbed model are determined by parameters that are closely related to the stochastic noises. Our work improves many existing studies in the field of mathematical epidemiology and provides new techniques to predict and analyze the dynamic behavior of epidemics.
