  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.
