Uma abordagem numérica para modelos populacionais considerando incerteza do tipo intervalar nas condições iniciais

Abstract

This work presents a comparative study between Zadeh’s extension principle and Sup - $J_0$ extension principle, in uncertainty propagation, focusing on populational models described by differential equations. In this study, it is considered that the initial conditions of the models are given by intervals, in order to incorporate the intrinsic uncertainty of the phenomenon. To this end, population dynamics models are studied using Euler numerical method, which is adapted to interval arithmetic. Specifically, three models are considered, Malthus, Verhust and Gompertz. Simulations are provided for each model in order to analyze the uncertainty propagation for both Zadeh's and $J_0$ sums. The obtained results corroborate the theoretical results, showing that Zadeh’s sum propagates uncertainty over time, whereas the Sup - $J_0$ extension principle reduces the uncertainty.