Free Final-Time Optimal Control for HIV Viral Dynamics

Abstract: In this paper, we examine a well-established model for HIV wild-type infection. The algorithm for steepest descent method for fixed final-time is stated and a modified method for free final-time is presented. The first type of cost functional considered, seeks to minimize the total time of therapy. An easy implementation for this problem suggests that it can be effective in the early stages of treatment as well as for individual-based studies, due to the "hit first and hit hard" nature of optimal control. An LQR based cost functional is also presented and the solution is found using steepest descent method. It suggests that the optimal therapy must remain high until the patient shows signs of recovery after which, the therapy gradually decreases. This is in line with the biomedical philosophy. Solution to a modified problem which includes a weight for total time is approximated using the modified algorithm. It shows a considerable drop in the total period. We conclude that, a decreased and optimized therapy period can help us increase efficiency as well as the turnover rate for patient care.