Mathematical modeling of bi-mode transmission of hepatitis B with media coverage

Abstract

This paper presents a bi-mode transmission model for hepatitis B, focusing on two primary transmission routes: blood transfusion and excessive intravenous drug use. We constructed the model and conducted a mathematical analysis,including the calculation of the basic reproduction number using the next-generation matrix method and identifying various equilibrium points. We established the stability of these equilibria using the Routh-Hurwitz method for local stability and the Castillo-Chavez method for global stability of the disease-free equilibrium, while the Lyapunov functional technique was applied for the endemic equilibrium. A local sensitivity analysis assessed theimpact of parameters in the basic reproduction number. Finally, numerical simulations were presented to confirm that our theoretical findings align with the numerical results.