An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic

Published version

Published version
Repository DOI

Change log
Authors
Fokas, A. S.; orcid: 0000-0002-5881-802X; email: tf227@cam.ac.uk 
Dikaios, N.; orcid: 0000-0001-9865-0260 
Yortsos, Y. C. 
Abstract

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached exponentially. However, epidemiological data from Europe suggest that this approach is algebraic. Indeed, accurate long-term predictions have been obtained via a forecasting model only if it uses an algebraic as opposed to the standard exponential formula. In this work, by allowing those parameters of the SEIR model that reflect behavioural aspects (e.g. spatial distancing) to vary nonlinearly with the extent of the epidemic, we construct a model which exhibits asymptoticly algebraic behaviour. Interestingly, the emerging power law is consistent with the typical dynamics observed in various social settings. In addition, using reliable epidemiological data, we solve in a numerically robust way the inverse problem of determining all model parameters characterizing our novel model. Finally, using deep learning, we demonstrate that the algebraic forecasting model used earlier is optimal.

Description

Peer reviewed: True

Keywords
deep learning, forecasting and mechanistic models, COVID-19 pandemic, SEIR model
Journal Title
Royal Society Open Science
Conference Name
Journal ISSN
2054-5703
Volume Title
10
Publisher
The Royal Society