Uncertainty quantification using probabilistic numerics: application to models in mathematical epidemiology

Probabilistic numerics (PN) is a framework for analysing numerical algorithms accounting for all sources of numerical errors, including errors due to both round off and the choice of numerical scheme. The goal of this work is to use a Bayesian-based PN method to illustrate the quantification of uncertainty in mathematical epidemiology modelling. We simultaneously account for the uncertainty in data, parameters, as well as numerical discretization in applying this framework to the data from an ongoing community-acquired Methicillin-resistant Staphylococcus aureus epidemic in Chicago.