IJPAM: Volume 59, No. 1 (2010)


Jose Marie Orellana
Department of Applied Mathematics
Conservatoire National des Arts et Metiers
292, Saint Martin Str., Paris, 75003, FRANCE
e-mail: jose.orellana@cnam.fr

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 Pontryaguine'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 five order scheme algorithm. Numerical solutions to the optimality system are obtained and related histories are shown. The possibility of scheduled treatment interruption is also examined.

Received: December 30, 2009

AMS Subject Classification: 92D30, 49K15, 34B15

Key Words and Phrases: Fixed-end-time optimization, HIV, mathematical model, multi-drug therapy, STI

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 1