METHODOLOGY TO DETERMINE THE EVOLUTION OF ASYMPTOMATIC HIV POPULATION USING FUZZY SET THEORY

Abstract

The aim of this paper is to o study the evolution of positive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome. For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an individual microscopic model. The first describes the evolution of the population whereas the second the evolution of HIV in each individual of the population. This methodology is suggested by the way that experts use to conduct public policies, namely, to act at the individual level to observe and verify the manifest population. The population model we address is a differential equation system whose transference rate from asymptomatic to symptomatic population is found through a fuzzy rule-based system. The transference rate depends on the CD4+ level, the main T lymphocyte attacked by the HIV retrovirus when it reaches the bloodstream. The microscopic model for a characteristic individual in a population is used to obtain the CD4+ level at each time instant. From the CD4+ level, its fuzzy initial value, and the macroscopic population model, we compute the fuzzy values of the proportion of asymptomatic population at each time instant t using the extension principle. Next, centroid defuzzification is used to obtain a solution that represents the number of infected individuals. This approach provides a method to find a solution of a non-autonomous differential equation from an autonomous equation, a fuzzy initial value, the extension principle, and center of gravity defuzzification. Simulation experiments show that the solution given by the method suggested in this paper fits well to AIDS population data reported in the literature.