Effects of sliding mode control antiretroviral drug on HIV-1 viral load

Human immunodeficiency virus (HIV) has devastating effects on human society. Researchers have proposed many models for the decay of CD 4(+) T cells, the growth of infected cells, and viral load. In this paper, four first-order nonlinear coupled differential equations have been considered. Four variables are CD 4(+) T cells, which are healthy, less infected cells, more infected cells capable of producing virus, and finally the viral load. Apart from the two drug therapies, protease inhibitor (PI) and reverse transcriptase inhibitor (RTI), which have already been considered in the literature, we have proposed antiretroviral drug (ARD) that works as sliding mode controller. We have used numerical methods to study the effect of RTI, PI, and ARD on healthy cells, infected cells, and the viral load. We have expressed our solutions in terms of log sigmoid functions and used memetic computing for the solution which is a hybridization of GA, a global optimizer, and sequential quadratic programming, a local optimizer. ARD, as a sliding mode controller, does help to improve the situation of the HIV patient, especially, in further reducing the viral load and also decreasing the infected cells which have the potential to produce virus. This helps in giving relief to the patient and an increase in life expectancy.