Analysis of Stochastic COVID-19 and Hepatitis B Co-infection Model with Brownian and Lévy Noise

Abstract

In this article, we formulate and analyze a mathematical model for the coinfection of HBV and COVID-19 that incorporates the effects of Brownian and Lévi noise. We studied the dynamics and effects of these diseases in a given population. First, we establish the basic reproduction number of the disease-free equilibrium point of the stochastic model by means of a suitable Lyapunov function. Additionally, we provided sufficient conditions for the stability of the model around the disease-free equilibrium points. Finally, using a few simulation studies, we demonstrate our theoretical results. In particularly, we derived threshold values for HBV only, COVID-19 only,, and co-infectionfor the stochastic model around disease-free equilibrium point. Next, the conditions for stability in the stochastic sense for HBV only, COVID-19 only submodels, and the full model are established. Furthermore, we devote our concentrated attention to sufficient conditions for extinction and persistence using each of these reproductive numbers. Finally, by using the Euler–Murayama scheme, we demonstrate the dynamics of the coinfection by means of numerical simulations.