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

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Résumé

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.

Mots-clés

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