Estudo da Estabilidade de um Modelo da Dinâmica do HIV com Parâmetros Intervalares dependendo do Tratamento Antirretroviral

Abstract

The aim of this work is to analyze the stability of a microscopic model for the dynamics of Human Immunodeficiency Virus (HIV) with antiretroviral treatment and two interval parameters. The model considers the following variables: infected and uninfected CD4+ T lymphocytes, free virus and CD8+ cytotoxic T lymphocytes (CTL). Antiretroviral treatment directly influences the infection rate of CD4+ T lymphocytes by the virus (β) and the reproduction rate of virus (k). In this approach, stability is analyzed via restricted interval arithmetic. Initially, the stability study is carried out considering β as an interval parameter and is rewritten as a function of θ1, 0 ≤ θ1 ≤ 1. In the literature, the variation intervals of β and k are determined when antiretroviral therapy is considered. The study of the stability of the system for the β interval was carried out with the value of k being the midpoint of the interval [0.0625,0.2]. The criteria used for the stability analysis are the Routh-Hurwitz criteria and the signs of the eigenvalues of the characteristic polynomial depending on the variation of β. Subsequently, the expansion of the values of k is studied, starting from the midpoint, considering this interval parameter as a function of θ2, 0 ≤ θ2 ≤ 1. For the analysis of the biological phenomenon with antiretroviral treatment, a Fuzzy Rule-Based System (FRBS) was constructed with the input variables being adherence to treatment by HIV-seropositive individuals and the potency of the drug administered to the individual. The FRBS output variables are θ1 e θ2, which determine the infection rate of CD4+ T lymphocyte by the virus and reproduction rate of virus, respectively. The results obtained are consistent with information in the literature when HIV-seropositive individuals receive antiretroviral treatment.