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.

中文翻译：

---

具有隔离策略、随机传播和 Lévy 干扰的 SIS 流行病学模型的渐近行为的新结果

传染病的传播是当今世界的一项重大挑战，尤其是在最近爆发的 2019 年冠状病毒病 (COVID-19) 之后。隔离策略是控制流行病传播的重要干预措施之一，可最大限度地减少感染者和易感者之间接触的可能性。在这项研究中，我们分析了隔离期间各种随机扰动对流行动态的影响。为此，我们提出了一个 SIQS 流行病模型，该模型结合了随机传输和 Lévy 噪声，以模拟小型和大型扰动。在适当的条件下，证明了一些有趣的渐近特性，即遍历性、均值持久性和疾病的灭绝。理论结果表明，扰动模型的动力学由与随机噪声密切相关的参数决定。我们的工作改进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动态行为的新技术。