Applying the stochastic Galerkin method to epidemic models with individualised parameter distributions

Abstract

There are many different models to help predict the likely course an epidemic will take. However, the parameters within these models are often not known with certainty. It is important for this uncertainty to be incorporated into these models to ensure accurate predictions. This article considers the stochastic Galerkin method to solve an sir model with uncertainty in its parameters. A data set from an influenza outbreak in a boarding school is then investigated. Rather than just finding the `best' values for the parameters, several possible probability distributions for the parameters in the sir model are determined. The stochastic Galerkin method is then used to determine the mean solution of the model as well as its variance.