Implementation of an optimal control for reducing individuals infected by hepatitis B virus

Abstract

Abstract Hepatitis B is an inflammatory liver disease caused by hepatitis B virus, whose spread can be contagious and becomes a serious world health problem. The spread of hepatitis B can be modeled using the Susceptible, Infected, and Recovered (SIR) model. This paper aims is to reduce individuals infected with hepatitis B virus by applyingoptimal control strategies. The SIR model is given optimal control with three control variables, namely health promotion, treatment, and vaccination. Optimal control form is determined by the Pontryagin Maximum Principle (PMP) method to minimize the number of infected individuals and the associated costs. The step of PMP method i.e. Identify the Lagrange multipliers, and then minimizea Hamiltonian function, further obtaine stationary conditions, and finally find an optimal control. The results of numerical simulations completed by the Runge-Kutta Order 4 show effectiveness in minimizing infected individuals. In addition, it can also maximize individual recovery by giving the proposed three control variables.