An Optimal Control Approach to HIV Immunology

Edilson F. Arruda¹, Claudia M. Dias², Camila V. de Magalhães³, Dayse H. Pastore³, Roberto C. A. Thomé³, Hyun Mo Yang⁴

¹Instituto Alberto Luiz Coimbra de Pós Graduação e Pesquisa de Engenharia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
²Instituto Multidisciplinar, Universidade Federal Rural do Rio de Janeiro, Nova Iguaçu, Brazil.
³Departamento de Matemática, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Rio de Janeiro, Brazil.
⁴Departamento de Matemática Aplicada, Universidade Estadual de Campinas, Campinas, Brazil.

DOI: 10.4236/am.2015.66102                

Abstract

This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account cells that represent two distinct mechanisms of the immune system in the defense against HIV: the non-HIV-activated cells and the HIV-activated cells. With a view at minimizing the side effects of a treatment that employs a drug combination designed to attack the HIV at various stages of its life cycle, we introduce control variables that represent the infected patient’s medication. The optimal control rule that prescribes the medication for a given time period is obtained by means of Pontryagin’s Maximum Principle.

Keywords

HIV, Mathematical Modelling, Optimal Control, Pontryagin’s Maximum Principle

Conflicts of Interest

The authors declare no conflicts of interest.

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