Abstract: Hepatitis B has become a major health threat because it is a life-threatening liver disease with an estimated 0.25 billion people suffering from this infectious disease worldwide. This paper presents a SLITR (Susceptible-Latent-Infectious-Treatment-Recovery) mathematical model that combines both vaccination and treatment as a means of controlling the hepatitis B virus (HBV). The nonlinear ordinary differential equations for the HBV transmission capacities were resolved and the basic reproduction number $$R_{0}$$ computed using the next generation matrix method and simulated numerically using the Runge-Kutta fourth order scheme implemented using MatLab. The stability points for disease-free equilibrium state (DFE), endemic equilibrium state (EE), and basic reproduction number $$R_{0}$$ were obtained and the results show that the disease-free equilibrium was both locally and globally asymptotically stable ($$R_{0}<1$$) . Similarly, treatment or vaccine administered was effective in alleviating the spread of HBV disease, and when both control strategies are combined, the diseases are quickly controlled and eventually eradicated.

Keywords: HBV, Disease, Latent, Vertical transmission, Infectious, Stability

Pages: 178-191