Model Persamaan Differensial Untuk Pengendalian Infeksi Virus Hepatitis B

Abstract

dI Hepatitis B is disease caused by the hepatitis B virus, can acute or chronic. In- fection with the hepatitis B virus (HBV) is a major health problem, which can lead to cirrhosis and primery hepatocellular carcinoma (HCC). The aim of this thesis is the application of optimal control for the system of ordinary differential equations modeling the Hepatitis B Virus (HBV) infection. Present a mathema- tical model of Hepatitis B Viral (HBV). The model contains tree variables, that is, uninfected target cells (T), infected cells (1) and free virions (V). HBV model dT is given by following linear system of differential equations =T- -ďT-(1- dt u1(t))ẞVT+us(t)VT, = (1 — u1(t))ẞVT — 81, = (1-u2(t))pl - cV. The optimal controls represent the efficiency of drug therapy in inhibiting viral pro- duction and preventing new infections. The control functions, u(t) and u(t), the control u2(t), represents the efficiency of drug therapy in inhibiting viral pro- duction, such that the virion production rate under therapy is (1-u2(t))p). The control u(t), represents the efficiency of drug therapy in blocking new infection, so that infection rate in the presence of drug is (1-u(t))B. The control us (t), represents disiplin to keep our neigh borhood. The Pontryagin's maximum priciple is used to characterize the optimal controls. The optimality system is derived and solved numerically.