Stochastic Analysis of COVID-19 Epidemics Under Quarantine Measures

Abstract

To enhance our understanding of the complex dynamics of the COVID-19 epidemic, we investigated a stochastic SIQS epidemic model that includes a compartment specifically for populations under quarantine. This study aims to examine the impact of environmental noise on the asymptotic properties of a stochastic variant of the classical SIQS epidemic model. Our model incorporates white noise, colored noise, and Lévy noise. Under certain parameter conditions, we demonstrate that the disease-free equilibrium state is globally asymptotically stable in probability. Furthermore, we establish the conditions under which the disease persists, considering the intensities of various noises, the model parameters, and the stationary distribution of the Markov chain. A key finding of our work is that our conditions are sufficient and nearly necessary to predict the extinction or persistence of the epidemic. Numerical simulations support the results presented.