Dynamics of Hepatitis B Virus Disease with Infectious Latent and Vertical Transmission

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 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 R0 were obtained and the results show that the disease-free equilibrium was both locally and globally asymptotically stable. 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.