Mathematical modeling of hepatitis B infection with vaccination and optimal control interventions

Abstract

In this paper, we formulate a mathematical model to analyze the impact of hospitalization and vaccination on the transmission dynamics of hepatitis B infection. Initially, we evaluate the model equilibria and basic reproduction number. Further, using Lyapunov function we prove that the model has a globally asymptotically stable infection free equilibrium when the basic reproduction number is less than 1, and using geometric approach we show global asymptotic stability of endemic equilibrium, when ${ℛ}_0>$ 1. We perform sensitivity analysis of ${ℛ}_0$ to identify the dominant parameters that seriously affect the hepatitis B infection. After that, using optimal control theory and Pontryagin’s maximum principle, we develop the control problem and illustrate the necessary optimality conditions. Finally, we perform the numerical simulations in order to point out the effectiveness of control interventions.