ABSTRACT
Recently, the pandemic of Covid-19 attacked many countries, and many public establishments were closed because of this pandemic. As well, the Covid-19 pandemic hurt the economy and various activities of countries around the world. Mathematical Modeling and numerical analysis can help governments to find solutions for controlling the propagation of the Covid-19 pandemic. In the present paper, we consider a stochastic Lévy jumps epidemic model that models the propagation of Covid-19 in a population divided into six groups of individuals. We investigate the extinction and persistence of our stochastic systems with and without Lévy jumps. Furthermore, we give a detailed numerical comparison of disease for the stochastic and deterministic systems. © 2022 the author(s).
ABSTRACT
In this paper, we propose a stochastic SIQR model and discuss the impact of Levy 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 Levy noises influence the transmission dynamic of the system.