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

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  • Jafelice, R.M.
  • Lodwick, W.A.

Abstract

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.

Suggested Citation

  • Jafelice, R.M. & Lodwick, W.A., 2021. "Interval analysis of the HIV dynamics model solution using type-2 fuzzy sets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 306-327.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:306-327
    DOI: 10.1016/j.matcom.2020.08.022
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    References listed on IDEAS

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    1. R. Motta Jafelice & C. A. F. Silva & L. C. Barros & R. C. Bassanezi, 2015. "A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-9, June.
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