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Journal of Applied Mathematics
Volume 2015, Article ID 378753, 9 pages
http://dx.doi.org/10.1155/2015/378753
Research Article

A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton

1Faculty of Mathematics, Federal University of Uberlândia, 38408-100 Uberlândia, MG, Brazil
2Faculty of Mechanical Engineering, Federal University of Uberlândia, 38408-100 Uberlândia, MG, Brazil
3Department of Applied Mathematics, IMECC, State University of Campinas, 13083-859 Campinas, SP, Brazil

Received 3 March 2015; Revised 12 May 2015; Accepted 14 May 2015

Academic Editor: Jianming Zhan

Copyright © 2015 R. Motta Jafelice et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objective of this research is to study the evolution of CD4+ T lymphocytes infected with HIV in HIV-seropositive individuals under antiretroviral treatment utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-dependent parameter with delay. Such delay is given by a fuzzy number due to the uncertainty of the effects of both pharmacological and intracellular delays. A cellular automaton is utilized to estimate the parameters of the system. The effects of antiretroviral therapy in the cellular automaton are modeled using a fuzzy rule-based system with two inputs: the medication potency and the treatment adhesion for three hypothetical individuals. For each of them, we determine the infection rate of CD4+ T lymphocytes, which is different from zero, as opposed to other studies reported in the literature. As the infection rate is considered a fuzzy parameter, we determine the fuzzy and the defuzzified solutions for the infected CD4+ T lymphocytes. We obtain the maximum values of infected cells for individuals that receive low, medium, and high potency medication and treatment adhesion. The results obtained are in accordance qualitatively with what would be expected in a real situation.