Math. Model. Nat. Phenom.
Volume 17, 2022
Coronavirus: Scientific insights and societal aspects
|Number of page(s)
|20 May 2022
Efficient Uncertainty Quantification and Variance-Based Sensitivity Analysis in Epidemic Modelling Using Polynomial Chaos
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
* Corresponding author: email@example.com
Accepted: 10 April 2022
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.
Mathematics Subject Classification: 62J10 / 65C60 / 92D30
Key words: Uncertainty quantiflctaion / global statistics / sobol indices / epidemic modelling / Covid-19
© The authors. Published by EDP Sciences, 2022
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