  Uncertainty in data is certainly one of the main problems in epidemiology, as
shown by the recent COVID-19 pandemic. The need for efficient methods capable
of quantifying uncertainty in the mathematical model is essential in order to
produce realistic scenarios of the spread of infection. In this paper, we
introduce a bi-fidelity approach to quantify uncertainty in spatially dependent
epidemic models. The approach is based on evaluating a high-fidelity model on a
small number of samples properly selected from a large number of evaluations of
a low-fidelity model. In particular, we will consider the class of multiscale
transport 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 simple
two-velocity discrete models for low-fidelity evaluations. Both models share
the same diffusive behavior and are solved with ad-hoc asymptotic-preserving
numerical discretizations. A series of numerical experiments confirm the
validity of the approach.
