Mathematical Model Of Hepatitis B Transmission Dynamics With Optimal Control

Abstract

In this thesis we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Initially we consider constant controls for vaccination and treatment. In the constant controls case, by determining the basic reproduction number, the basic reproductive number, R0 of our SVLICRS model was calculated to be 2.467198, which implies that on average, each infectious individual transmits virus to 2.467198 people, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize the number of acutely infected, Chronic carriers humans and the associated costs. Finally at the end numerical simulation results show that vaccination and treatment are the most effective way to control hepatitis B virus infection.