A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton

Abstract EN

The objective of this research is to study the evolution of CD4+ T lymphocytesinfected with HIV in HIV-seropositive individuals under antiretroviral treatmentutilizing a mathematical model consisting of a system of delay-differential equations.

The infection rate of CD4+ T lymphocytes is a time-dependent parameterwith delay.

Such delay is given by a fuzzy number due to the uncertainty of theeffects of both pharmacological and intracellular delays.

A cellular automaton isutilized to estimate the parameters of the system.

The effects of antiretroviral therapy in the cellular automaton are modeled using a fuzzy rule-based system withtwo inputs: the medication potency and the treatment adhesion for three hypothetical individuals.

For each of them, we determine the infection rate of CD4+ Tlymphocytes, which is different from zero, as opposed to other studies reported inthe literature.

As the infection rate is considered a fuzzy parameter, we determine thefuzzy 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 inaccordance qualitatively with what would be expected in a real situation.