Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Epidemic models with random coefficients
Mathematical and Computer Modelling: An International Journal
Biofilm growth on medical implants with randomness
Mathematical and Computer Modelling: An International Journal
Analytic and numerical solutions of a Riccati differential equation with random coefficients
Journal of Computational and Applied Mathematics
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In the mathematical modeling of population growth, and in particular of bacterial growth, parameters are either measured directly or determined by curve fitting. These parameters have large variability that depends on the experimental 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 work the parameters that appear in the Monod kinetics growth 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.