Asymptotic properties of a stochastic SIQR epidemic model with Lévy Jumps and Beddington-DeAngelis incidence rate

Abstract

In this paper, we propose a stochastic SIQR model and discuss the impact of Lévy jumps and Beddington-DeAngelis incidence rate on the transmission of diseases. We prove that our proposed model admits a unique global positive solution and an invariant positive set. We establish sufficient conditions for the extinction and persistence of the disease in the population using some stochastic calculus background. We illustrate our theoretical results by numerical simulations. We infer that the white and Lévy noises influence the transmission dynamic of the system.