The SI epidemiological model with interactive fuzzy parameters

We study the SI epidemiological model in two distinct ways, one considering correlation between the numbers of susceptible and infected individuals, and another assuming that the initial conditions and the transmission rate are interactive. In both cases we assume uncertainties given by fuzzy sets. Interactivity is based on the concept of completely correlated fuzzy numbers. The dynamics of each model is represented by fuzzy differential equations (FDE) approached in two ways: the first using the theory of fuzzy differential inclusion and the second using Zadeh´s extension principle to obtain a solution. We found that both produce the same solution.