Dynamic optimization algorithms to mitigate HIV escape

More than 25 years since HIV was discovered, a cure for infection remains to be found. One main concern in treating HIV infection is the emergence of resistant genotypes, causing the patient to proceed to AIDS. In this paper, we consider a specific simplified switched system model of HIV mutation dynamics with four genotypes under two different treatments. We address the optimal control problem for a general class of switched systems to find the drug sequence that minimizes the viral load. This gives a two point boundary value problem, that is difficult to solve due to the switched system nature. Alternatively, exhaustive search approaches may be used but are computationally prohibitive. To avoid these problems we propose several algorithms based on linear programming to reduce the computational burden whilst still computing the optimal sequence.