Covid-19 Modelling, estimation and prediction
Author
Barrios Blaya, Borja
Term
4. term
Education
Publication year
2021
Submitted on
2021-06-03
Pages
72
Abstract
This thesis develops a deterministic (rule-based) mathematical model of COVID-19 to estimate and forecast how the epidemic evolved in Denmark. To combine the model with real-world observations, we use the Extended Kalman Filter (EKF), an algorithm that handles non-linear relationships by fusing model predictions with noisy data to estimate unobserved quantities (states). We calibrate and test the model using data from the Danish health authorities. We evaluate performance over both short and long time horizons to show that the approach can adapt to different time frames. The method is applied to each Danish region to estimate the course of the pandemic locally. To illustrate forecasting, we produce a 40-day projection of hospitalizations in the Capital Region of Denmark (Region Hovedstaden) and examine how the model behaves when, after the EKF prediction step, no new measurements are used to correct the forecast. Overall, the results indicate that the model reproduces key features of COVID-19 dynamics in Danish society. However, some parts of the modeling rely on assumptions, which should be examined further.
Denne afhandling udvikler en deterministisk (regelbaseret) matematisk model af COVID-19 med det formål at estimere og forudsige, hvordan epidemien udviklede sig i Danmark. For at kombinere modellen med virkelige observationer anvendes Extended Kalman Filter (EKF), en algoritme der håndterer ikke-lineære sammenhænge ved at sammenholde modellens forudsigelser med støjende data for at estimere ikke-observerede størrelser (tilstande). Modellen kalibreres og testes med data fra de danske sundhedsmyndigheder. Vi vurderer ydeevnen over både korte og lange tidshorisonter for at vise, at tilgangen kan tilpasses forskellige tidsrammer. Metoden anvendes på hver dansk region for at estimere, hvordan pandemien forløb lokalt. For at illustrere fremskrivning udarbejdes en 40 dages prognose for indlæggelser i Region Hovedstaden, og vi undersøger, hvordan modellen opfører sig, når der efter EKF'ens forudsigelsestrin ikke bruges nye målinger til at korrigere prognosen. Samlet set tyder resultaterne på, at modellen kan gengive centrale træk ved COVID-19's udvikling i det danske samfund. Nogle dele af modelleringen bygger dog på antagelser, som bør undersøges nærmere.
[This apstract has been rewritten with the help of AI based on the project's original abstract]
Keywords
Covid ; Modelling ; Estimation ; Prediction ; Model ; Kalman