Mathematical Modelling and Analysis of Stochastic COVID-19 and Hepatitis B Co-Infection Dynamics

Abstract

The recent resurgence of COVID-19 in a Hepatitis B virus some endemic countries could lead to adverse outcomes. In this article, we formulate and analyse a mathematical model to explains the co-infection dynamics of Hepatitis B virus and COVID-19. Our aim is to investigate the effect of Hepatitis B virus prevention, COVID-19 prevention, COVID-19 vaccination, and environmental factors on transmission dynamics, and formulate conditions for extinction and persistence of the diseases. First, we derive the basic reproduction number for HBV only, COVID-19 only, and co-infection stochastic models using the next-generation matrix method. Next, we establish the conditions for stability in the stochastic sense for HBV only, COVID-19 only sub-models, and the co-infection model using suitable Lyapunov functions. Furthermore, we devote our attention to finding sufficient conditions for extinction and persistence. Finally, motivated by Ghana data, we applied the Euler–Murayama scheme to illustrate the dynamics of the co-infection, COVID-19, HBV, and the effect of some parameters on disease transmission dynamics by means of numerical simulations.