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In this work we are study the Fuzzy Initial Value Problem (FIVP) with parameters and/or initial conditions given by fuzzy sets. Starting from the flow equation of the deterministic Initial Value Problem (IVP) associates to FIVP, we obtain the FIVP flow, through the principle of Zadeh. Follow, we introduce the concept of fuzzy equilibrium stability of FIVP and some examples are given.

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This article discusses the theory of constraint interval solutions to interval nonlinear initial value problems and applies the notion of constraint interval solutions to analyze the asymptotic behavior of a susceptible-infected-recovered (SIR) epidemiological nonlinear differential equation model, specifically the covid pandemic, in the presence of interval uncertainty to illustrate the efficacy of this approach. Furthermore, constraint interval solutions are used to estimate the intervals for the parameters by fitting solutions to the Brazilian’s Sars-Cov-2 pandemic official data. Simulations and graphical solutions incorporating constraint interval uncertainties are presented to help in the visualization of the pandemic’s behavior.

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