Optimal control in a multi-pathways HIV-1 infection model: a comparison between mono-drug and multi-drug therapies

Abstract

A multi-pathways HIV-1 infection model is analysed with three controls. First we prove the local and global stabilities of the disease-free and infected steady states when all three controls are constant. In the second phase, we consider the controls as time dependent and define a suitable optimal control problem. An objective function is characterised based on maximizing the healthy cells counts and minimizing the count of infected cells along with other systemic cost of drug therapy. Using Pontryagin's maximum principle, we give the necessary conditions for optimal control. Through numerical simulations, we investigate and compare the effect of different mono- and multi-drug therapies. In case of mono blockers, results show that the drug which blocks cell-to-cell dissemination of infection is a better option for treating an HIV-1 infected individual. In case of multi blockers, combined drug that contains cell-to-cell blocker and protease inhibitors controls the infection efficiently.