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
[1] 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.
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2 N OPTIMAL CONTROL APPROACH TO HIV IMMUNOLOGY- COMPUTATIONAL ASPECTS
[2] 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).
[3] 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).
[4] 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).