Aplicações da extensão de Zadeh na dinâmica do HIV com retardo fuzzy sob tratamento antirretroviral

Abstract

Mathematical models as applied to biological phenomena are usually involved with uncertainties. One way of determining solutions of such mathematical models, including their uncertainties, is by applying the Zadeh's extension principle, which is part of the fuzzy set theory. In this context, the general objective of this research is to present applications of the one-dimensional and two-dimensional Zadeh's extension principle on two mathematical models that simulate the dynamics of HIV antiretroviral treatment, with delay, in seropositive individuals. These applications are presented through fuzzy solutions of the proposed models of HIV dynamics, in which the delay and death rate of the virus are considered as fuzzy numbers. In the first model, the delay and the mortality rate of the virus are considered as fuzzy numbers correlated through an injective and monotonous function which facilitates the attainment of a fuzzy solution of the presented model, since it turns the two-dimensional Zadeh's extension principle into an one-dimensional type. The function that correlates the fuzzy parameters is estimated by two different methods, the first is Mamdani inference method and the second is Takagi-Sugeno inference method, which motivated a comparative study of the solutions in terms of the absolute error. In the other model, a numerical fuzzy solution is obtained through an algorithm developed in this work, considering in the model as triangular fuzzy numbers, the delay and the mortality rate of the virus that do not use a function that correlates them.