Kontrol Optimum Virus HIV Melalui Penggunaan Dua Jenis Obat

Abstract

This paper studied a mathematical interactions model of healthy CD4+T cells with HIV cells by involving two types of control strategies, i.e. increasing body’s immune drugs and using antiviral drugs. The interaction problem is formulated in term of optimal control model, where the objective functional is maximizing the population of healthy CD4+T cells and to minimize the systematic cost of using drugs. Application of Pontryagin maximum principle provides four differential equations as solution conditions: two differential equations for the system and two differential equations for the adjoint function. Next, applications of Berkovitz conditions provide two optimal control functions. Numerical solution was conducted using the 4th order Runge-Kutta method. Application of control to the system makes the population of healthy CD4+T cells increase and the HIV cells population decrease. As the larger weight in the control of immune drugs increase cause decrease in healthy CD4+T cells growth rate. It indicates that a larger weight provides negative effects on the body, so that drugs administration would be reduced.