Optimal control of hepatitis b virus disease in a population with infected immigrants

Abstract

This paper firstly presents a nonlinear extended deterministic model for assessing the impact of immigration on the spread of the Hepatitis B Virus (HBV) pandemic in a population with acute and chronic groups. This model studies the impact of optimal control on the treatment of immigrants and vaccination of HBV on the transmission dynamics of the disease in a homogeneous population with constant immigration. First, we derived the condition in which disease free equilibrium is locally and globally asymptotically stable. Second, we investigated by formulating the costs function problem as an optimal control problem, and we then use the Pontryagins Maximum Principle to solve the optimal control problems. The impact of each control mechanism individually and the combinations of these strategies in the control of HBV is also investigated. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and vaccination of infected immigrants on the spread of the disease with acute and chronic group.