Applying the stochastic Galerkin method to epidemic models with uncertainty in the parameters.
Parameters in modelling are not always known with absolute certainty. In epidemic modelling, this is true of many of the parameters. It is important for this uncertainty to be included in any model. This paper looks at using the stochastic Galerkin method to solve an SIR model with uncertainty in the parameters. The results obtained from the stochastic Galerkin method are then compared with results obtained through Monte Carlo sampling. The computational cost of each method is also compared. It is shown that the stochastic Galerkin method produces good results, even at low order expansions, that are much less computationally expensive than Monte Carlo sampling. It is also shown that the stochastic Galerkin method does not always converge and this non-convergence is explored.
School of Natural Sciences, Griffith University, 170 Kessels Road, Nathan, Queensland 4111, Australia. Electronic address: david.harman@griffithuni.edu.au.
David B
DB
Harman
School of Natural Sciences, Griffith University, 170 Kessels Road, Nathan, Queensland 4111, Australia. Electronic address: p.johnston@griffith.edu.au.
Peter R
PR
Johnston
D003141:Communicable Diseases; D006801:Humans; D008962:Models, Theoretical; D013269:Stochastic Processes; D035501:Uncertainty
Infectious disease; Non-convergence; Polynomial chaos; Sobol index; Uncertainty quantification