An epidemiological model for HIV infection in a population using type-2 fuzzy sets and cellular automaton

Abstract

Acquired immunodeficiency syndrome (AIDS) is an infectious and contagious disease caused by the human immunodeficiency virus (HIV), which is a global health problem. This study presents a cellular automaton (CA) model of HIV that uses an adaptation of the system of ordinary differential equations proposed by Anderson et al. (J Math Appl Med Biol 3:229–263, 1986) and an interval type-2 fuzzy rule-based system (FRBS). The aim of this study is to show that this CA model is consistent with known statistical results of HIV patients. The novelty of this research is not only the use of CA with a type-2 FRBS to model the HIV in a way that is consistent with the data, its adaptation and improvement of the standard dynamical system model of Anderson et al. (J Math Appl Med Biol 3:229–263, 1986) by adding three phases of viral evolution of the HIV infection in the absence of antiretroviral treatment. One of the features of the CA is its randomness due to the movement of its cells, the infection period in which the individuals are, the places and partners that represent the activity of the HIV population. This feature is efficiently modeled using FRBS with interval type-2 fuzzy sets. The output of our model favorably compares to the data from the period of 1980–1995, when the use of antiretroviral drug was not available.