Modelo Dinâmico Regulatório de Glicose-Insulina e Robustez Sob a Ação de Perturbações Externas

Abstract

The metabolic disorder Diabetes Melittus is characterized by high levels of glucose in the bloodstream and in the quest to understand how the glucose-insulin interaction happens, the article by Shabestari and collaborators (SHABESTARI et al., 2018) proposed a non-linear mathematical model based on a predator-prey model with cubic functions added, constituting a non-linear dynamic system of chaotic dynamics, verified by the calculated values of the Lyapunov exponents. The chaotic dynamics is analyzed through the bifurcation diagram and the diagram of the Lyapunov exponents in a certain range of model parameters, the main ones being a1, a7, a8 e a15 that represent, in that order, hypoglycemia, hyperinsulinemia, Type 1 Diabetes and Type 2 Diabetes. Other analyzes performed were: Boxplot calculation to compare real data with data from the mathematical model; parameter space diagrams to characterize the dynamic behavior of the model; parametric perturbations to study the effect on dynamic changes in the model; attraction basin diagrams with and without parametric perturbations for the study of basin boundaries and calculation of the uncertainty exponent for boundary with fractal structure. It was verified that the chaotic behavior was suppressed for different amplitudes and frequencies of the perturbation. In the simulations, basins of attraction were discovered whose boundaries have fractal structures in the glucose-insulin system under parametric perturbations.