AN OPTIMAL CONTROL APPROACH TO HIV IMMUNOLOGY- COMPUTATIONAL ASPECTS Claudia Mazza Dias1 , Roberto Carlos Antunes Thomé, Dayse Haime Pastore 2 , Edilson Fernandes de Arruda3 1 Departamento de Tecnologias e Linguagens - Instituto Multidisciplinar Universidade Federal Rural do Rio de Janeiro Av. Governador Roberto Silveira, s/n, Moquetá , CEP:26020-740, Nova Iguaçu, RJ, Brasil [email protected] 2 Centro Federal de Educação Tecnológica Celso Suckow da Fonseca Av. Maracanã, 229, CEP: 20271-110, Rio de Janeiro, RJ, Brasil [email protected], [email protected] 3 Programa de Engenharia de Produção Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia, Universidade Federal do Rio de Janeiro Centro de Tecnologia, Bloco F, sala 103, Ilha do Fundão. Caixa Postal 68507, Rio de Janeiro, RJ, 21941-972, Brasil [email protected] Abstract The work addresses a model for the spread of HIV in the human body and proposes a strategy to minimize the computational cost of solving this model via the finite difference method (FDM). The model comprises a set of nonlinear ordinary differential equations that describe the dynamics of susceptible, infected, defense, active cells and HIV. It is innovative in that it minimizes the side effects of medication by introducing a time variable to control the treatment of the infected patient, obtaining an optimal medication strategy. In addition, the proposed strategy makes use of a dynamic refinement of the FDM grid which, in turn, applies properties of linearly convergent algorithms to derive an optimal sequence of approximate models with respect to the cumulative computational cost. The derived sequence converges to the real model and minimizes the time to find the solution, resulting in significant computational savings. References  A. Almudevar, and E. F. Arruda, Optimal Approximation Schedules for a Class of Iterative Algorithms with an Application to Multigrid Value Iteration, IEEE Transactions on Automatic Control. 57, 12(2012), pp. 3132-3146. A 2 N OPTIMAL CONTROL APPROACH TO HIV IMMUNOLOGY- COMPUTATIONAL ASPECTS  E. F. Arruda, C. M. Dias, D. H. Pastore, R. C. A. Thomé, A Computational Cost Optimization Strategy for the Numerical Solution of HIV Dynamics, Proceedings of XXXV Iberian Latin-American Congress on Computational Methods in Engineering, Evandro Parente Jr (Editor), ABMEC, Fortaleza, CE, Brazil, November 23-26 (2014).  C. M. Dias and E. F. Arruda, Computational Cost Optimization for Influenza A (H1N1) Epidemic Model. Proceedings of the 7th International Congress on Environmental Modelling and Software, June 15-19, San Diego, California, USA. ISBN: 978-88-9035-744-2 (2014).  C. V. Magalhães, R. C. A. , Thomé, D. H. Pastore, H. M. Yang, An Optimal Control Approach to HIV Immunology. Proceedings of the XXXIV Iberian Latin-American Congress on Computational Methods in Engineering, Z.J.G.N Del Prado (Editor), ABMEC, Pirinópolis, GO, Brazil, November 10-13 (2013).