Efficient Uncertainty Quantification and Variance-Based Sensitivity Analysis in Epidemic Modelling Using Polynomial Chaos

Bjørn C.S. Jensen¹ ; Allan P. Engsig-Karup² ; Kim Knudsen²

¹ Department of Mathematics and Statistics, University of Helsinki, 00560 Helsinki, Finland
² Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark

Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 8.

Résumé

The use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitations. We propose to do efficient uncertainty quantification in compartmental epidemic models using the generalized Polynomial Chaos (gPC) framework. This framework uses a suitable polynomial basis that can be tailored to the underlying distribution for the parameter uncertainty to do forward propagation through efficient sampling via a mathematical model to quantify the effect on the output. By evaluating the model in a small number of selected points, gPC provides illuminating statistics and sensitivity analysis at a low computational cost. Through two particular case studies based on Danish data for the spread of Covid-19, we demonstrate the applicability of the technique. The test cases consider epidemic peak time estimation and the dynamics between superspreading and partial lockdown measures. The computational results show the efficiency and feasibility of the uncertainty quantification techniques based on gPC, and highlight the relevance of computational uncertainty quantification in epidemic modelling.

Détail

DOI : 10.1051/mmnp/2022014

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