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 the
impact of parameters in the basic reproduction number. Finally, numerical simulations were presented to confirm
that our theoretical findings align with the numerical results.

Hepatitis, Media coverage, Mathematical study, Herd immunity, Numerical simulation