Effect of HAART on CTL mediated immune cells: An optimal control theoretic approach

Abstract

Highly active antiretroviral therapy (HAART) reduces the virus load during long term drug therapy. It is observed that during drug therapy virus load sustained in the immune system also CTL is generated due to activation of immune cells and declination of memory CTL which is actually the causal effect of suppression of virus load. Here we extended our work (Roy PK, Chatterjee AN (2010) Lecture notes in engineering and computer science: proceedings of the World Congress on engineering 2010, pp 615-620) and formulate a set of differential equations to study the effect of HAART on immune cells to a HIV infected individuals. We also incorporate in our model of an optimal control strategy during drug treatment, which reduces the infected cell population and increases the uninfected cell population. It is to be mentioned here that the control variable is used as drug dose which introduces in the diseases transmission term. Analytical and numerical study shows that optimal control process can reduces the infected cell population. An objective function is also introduced to minimize the systemic cost of chemotherapy. © 2011 Springer Science+Business Media B.V.