Abstract
Highly Active Anti-Retroviral Therapies (HAART) have proven to be extremely effective in improving and prolonging the patient's life. Though, a concern arises since a long term drug intake induces many strong sides effects and reduces reactivity of the virus to any therapy. The purpose of the paper is to use numerical analysis and optimization tools to suggest improved therapies to handle HIV infection. The evolution of the infection is modelled by an ordinary differential equation system which includes both immune response and multi-drug effects. For a fixed time, one looks for a two drugs control strategy based on Pontryagine's minimum principle with an objective function which takes into account three contributions: the viral load, the transient evolution of infection and the quantities of drug used. Simulations are carried out using an indirect optimization method along with Runge–Kutta adaptative stepsize algorithm. Numerical solutions to the optimality system are obtained and related histories are shown. The possibility of Scheduled Treatment Interruption is also examined.
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