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

Giulia Bertaglia, Liu Liu, Lorenzo Pareschi*, Xueyu Zhu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
12 Downloads (Pure)

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 [13, 7] as the high-fidelity reference and use simple two-velocity discrete models for lowfidelity 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.

Original languageEnglish
Pages (from-to)401-425
Number of pages25
JournalNetworks and Heterogeneous Media
Volume17
Issue number3
DOIs
Publication statusPublished - Jun 2022

Keywords

  • asymptotic-preserving schemes
  • Bi-fidelity methods
  • diffusion limit
  • epidemic models
  • kinetic transport equations
  • uncertainty quantification

ASJC Scopus subject areas

  • Statistics and Probability
  • General Engineering
  • Computer Science Applications
  • Applied Mathematics

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