Dynamic modelling of Hepatitis B and use of optimal control to reduce the infected population and minimizing the cost of vaccination and treatment

Abstract

Hepatitis B infection that leads to chronic stage can be life threatening to human, for prevention it is necessary to conduct treatment and vaccination. Conducting treatment and vaccination are controls variables that will be applied to the dynamic modelling of Hepatitis B using Pontryagin Minimum Principle. The present paper will describe model formulation of Hepatitis B, analyzing direction of the equilibrium, Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE), which can be done by determining dimensionless number of R0 (Basic Reproduction Number). Furthermore we use Pontryagin Minimum Principle to find optimal solution of the control. The purpose of optimal control is to minimize the number of acute and chronic infected population and values (cost) of vaccination and treatment. Numerical calculations also performed to illustrate the graph.