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Uncertainty in data is certainly one of the main problems in epidemiology, asshown by the recent COVID-19 pandemic. The need for efficient methods capableof quantifying uncertainty in the mathematical model is essential in order toproduce realistic scenarios of the spread of infection. In this paper, weintroduce a bi-fidelity approach to quantify uncertainty in spatially dependentepidemic models. The approach is based on evaluating a high-fidelity model on asmall number of samples properly selected from a large number of evaluations ofa low-fidelity model. In particular, we will consider the class of multiscaletransport models recently introduced in Bertaglia, Boscheri, Dimarco &Pareschi, Math. Biosci. Eng. (2021) and Boscheri, Dimarco & Pareschi, Math.Mod. Meth. App. Scie. (2021) as the high-fidelity reference and use simpletwo-velocity discrete models for low-fidelity evaluations. Both models sharethe same diffusive behavior and are solved with ad-hoc asymptotic-preservingnumerical discretizations. A series of numerical experiments confirm thevalidity of the approach.

Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties