Interval analysis of the HIV dynamics model solution using type-2 fuzzy sets

The objective of this study is to analyze the numerical intervals of the Human Immunodeficiency Virus (HIV) using the solution of a dynamics model at each time iteration, considering the infection rate of CD4+ T lymphocytes and the production rate of the virus as outputs of an interval type-2 Fuzzy Rule-Based System (FRBS). The mathematical model consists of a system of ordinary differential equations in the case of the HIV-seropositive individuals who are under antiretroviral treatment. The input variables of FRBS are adherence to treatment and medication potency, which are important factors in the treatment of HIV-seropositive individuals. If the infection rate of CD4+ T lymphocytes and the production rate of the virus are output variables of a type-1 FRBS, then we obtain curves for the solution of the HIV dynamic model. When the rates are outputs obtained through the interval type-2 FRBS, we can obtain ranges. This means that a type-2 FRBS provides more information about the behavior of the uninfected and infected CD4+ T lymphocytes, free virus particles, and virus-specific cytotoxic T lymphocytes (CTL) that attack infected cells in the bloodstream of a HIV-seropositive individual. The theory of the single level constraint interval arithmetic allows us to obtain a single interval that containing the intervals of all iterations for uninfected and infected CD4+ T lymphocytes, free virus particles, and CTL. Thus, the novel contribution of this research is twofold. Firstly, the use of interval type-2 fuzzy rule-base analysis to obtain more informative and robust results not possible with standard approaches is new. Secondly, the use of the fuzzy constraint interval representation for fuzzy type-2 intervals in the context of the type-2 fuzzy rule base is new. Moreover, constraint intervals unify the theory and its use in single-level constraint representations simplifies the calculations, though this aspect is not pursued in detail here. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.