The dynamics of hepatitis B virus via a stochastic epidemic model

Hepatitis B is a highly contagious disease affecting approximately two billion people globally. Mathematical modeling of hepatitis B virus (HBV) transmission is crucial not only for understanding its current spread but also for predicting future dynamics. In this study, we develop a stochastic differential equation (SDE) model that captures the key characteristics of HBV transmission, acknowledging its inherent randomness. The model incorporates two infectious compartments: acutely infected and chronically infected individuals, reflecting the clinical significance of both groups. Notably, some individuals may progress directly to the chronic stage without a prior acute phase. Successfully vaccinated individuals are considered recovered, given that the hepatitis B vaccine provides protective immunity in approximately 95% of cases. We establish the model’s well-posedness by proving the existence and uniqueness of solutions, and we analyze conditions for disease extinction and persistence. Sensitivity analysis is also performed to evaluate the impact of key epidemiological parameters on disease dynamics. Finally, numerical simulations are conducted using the stochastic Runge–Kutta (SRK) method to validate and support the analytical findings.