A stochastic hepatitis B model with media coverage and Lévy noise

Globally, it is evident that vaccination and social media significantly influence the spread of diseases. Research has demonstrated that the spread of diseases can be affected by unforeseen events. Therefore, a stochastic hepatitis B virus (HBV) dynamical model is constructed that incorporates media coverage, while also Lévy noise is included. Itô's formula and the Lyapunov function approach are employed to analyze the existence of a positive global solution. Furthermore, the necessary conditions for disease eradication as well as long-term survival are also established to facilitate the general understanding. The statistics indicate that the media's impact is not immediate and does not lead to disease eradication. To effectively manage the spread of diseases, it is essential to employ a combination of significant noise disruption and a low rate of decline in vaccine effectiveness. Numerical simulations are conducted to demonstrate the analytical findings.