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

TL;DR

This paper introduces a bi-fidelity stochastic collocation method to efficiently quantify uncertainty in spatial epidemic transport models, combining high- and low-fidelity models for accurate and computationally feasible analysis.

Contribution

The paper presents a novel bi-fidelity approach using multiscale transport models and simple two-velocity models to efficiently quantify uncertainty in epidemic spread simulations.

Findings

Numerical experiments confirm the method's validity.

The approach reduces computational cost while maintaining accuracy.

Effective in modeling uncertainties in epidemic transport scenarios.

Abstract

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.