Epidemic models with random coefficients

Mathematical models are very important in epidemiology. Many of the models are given by differential equations and most consider that the parameters are deterministic variables. But in practice, these parameters have large variability that depends on the measurement method and its inherent error, on differences in the actual population sample size used, as well as other factors that are difficult to account for. In this paper the parameters that appear in SIR and SIRS epidemic model are considered random variables with specified distributions. A stochastic spectral representation of the parameters is used, together with the polynomial chaos method, to obtain a system of differential equations, which is integrated numerically to obtain the evolution of the mean and higher-order moments with respect to time.