A Fuzzy Delay Differential Equation Model for HIV Dynamics

This paper presents a process to obtain the solution (or flux) of a fuzzy delay system and to determine the fuzzy expected curve for the HIV (human immunodeficiency virus) when HIV-positive individuals receive antiretroviral therapy. This delay is defined as the time between the infection of a CD4+ type T-lymphocyte cell by the virus and the production of new virus particles. The intracellular delay is represented by an uncertainty parameter that depends on the individual characteristics of HIV-positive patients. A fuzzy rulebased system is used to model this parameter. The solution of the system of delay differential equations, which is a fuzzy process, is obtained from Zadeh’s Extension Principle. Lastly, for each instant t, we calculate the fuzzy expected value obtained by the Center of Gravity. Keywords— Delay Differential Equation; Epidemiological Modeling; Fuzzy Expected Value; Fuzzy Set; HIV Dynamics; Mamdani Controller.