New results on the asymptotic behavior of an SIS epidemiological model with quarantine strategy, stochastic transmission, and L\'evy disturbance

TL;DR

This paper investigates the long-term behavior of an SIS epidemic model with quarantine, stochastic transmission, and Levy noise, providing new insights into disease persistence and extinction under random disturbances.

Contribution

It introduces a stochastic SIQS model with Levy noise and proves asymptotic properties like ergodicity, persistence, and extinction, advancing mathematical epidemiology methods.

Findings

Model exhibits ergodicity under certain conditions

Disease can persist or go extinct depending on noise parameters

Provides new techniques for analyzing stochastic epidemic dynamics

Abstract

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 L\'evy 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.