Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Mathematics of Infectious Diseases
SIAM Review
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Random coefficient differential equation models for bacterial growth
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
A comparative study of the numerical approximation of the random Airy differential equation
Computers & Mathematics with Applications
Analytic and numerical solutions of a Riccati differential equation with random coefficients
Journal of Computational and Applied Mathematics
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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.