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Open AccessArticle

Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19

1
Centre de Mathématiques Laurent-Schwartz, École Polytechnique Cour Vaneau, 91120 Palaiseau, France
2
Torus Actions SAS, 3 Avenue Didier Daurat, 31400 Toulouse, France
3
Ecole Nationale de l’Aviation Civile, 7 Avenue Edouard Belin, 31400 Toulouse, France
4
Institute of Mathematics of the Czech Academy of Sciences, Zitna 25, 11567 Praha 1, Czech Republic
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Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), Englerstr. 2, D-76131 Karlsruhe, Germany
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Institut de Mathematiques de Toulouse, Université Toulouse 3, 18 Route de Narbonne, 31400 Toulouse, France
*
Author to whom correspondence should be addressed.
Current address: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Campus Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris, France.
Invited fellow at Max Planck Institute, Bonn.
Biology 2020, 9(12), 477; https://doi.org/10.3390/biology9120477
Received: 19 November 2020 / Revised: 13 December 2020 / Accepted: 15 December 2020 / Published: 18 December 2020
(This article belongs to the Special Issue Theories and Models on COVID-19 Epidemics)
Using tools from both mathematics (especially wavelet theory) and computer science (machine learning), we present a general new method for modelling the evolution of epidemics which is not restricted to human populations. A crucial novel feature of our approach is that it significantly takes into account that an epidemic may take place in certain types of waves which cannot only be of a global as well as local nature, but can also occur at multiple different times and locations. In the particular case of the current Covid-19 pandemic, based on recent figures from the Johns Hopkins database we apply our model to France, Germany, Italy, the Czech Republic, as well as the US federal states New York and Florida, and compare it and its predictions to established as well as other recently developed forecasting methods and techniques.
We introduce the concept of epidemic-fitted wavelets which comprise, in particular, as special cases the number I(t) of infectious individuals at time t in classical SIR models and their derivatives. We present a novel method for modelling epidemic dynamics by a model selection method using wavelet theory and, for its applications, machine learning-based curve fitting techniques. Our universal models are functions that are finite linear combinations of epidemic-fitted wavelets. We apply our method by modelling and forecasting, based on the Johns Hopkins University dataset, the spread of the current Covid-19 (SARS-CoV-2) epidemic in France, Germany, Italy and the Czech Republic, as well as in the US federal states New York and Florida. View Full-Text
Keywords: Covid-19; SARS-CoV-2; epidemic-fitted wavelet; epidemic dynamics; model selection; curve fitting; Covid-19 spread predicting Covid-19; SARS-CoV-2; epidemic-fitted wavelet; epidemic dynamics; model selection; curve fitting; Covid-19 spread predicting
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MDPI and ACS Style

Tat Dat, T.; Frédéric, P.; Hang, N.T.T.; Jules, M.; Duc Thang, N.; Piffault, C.; Willy, R.; Susely, F.; Lê, H.V.; Tuschmann, W.; Tien Zung, N. Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19. Biology 2020, 9, 477. https://doi.org/10.3390/biology9120477

AMA Style

Tat Dat T, Frédéric P, Hang NTT, Jules M, Duc Thang N, Piffault C, Willy R, Susely F, Lê HV, Tuschmann W, Tien Zung N. Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19. Biology. 2020; 9(12):477. https://doi.org/10.3390/biology9120477

Chicago/Turabian Style

Tat Dat, Tô; Frédéric, Protin; Hang, Nguyen T.T.; Jules, Martel; Duc Thang, Nguyen; Piffault, Charles; Willy, Rodríguez; Susely, Figueroa; Lê, Hông V.; Tuschmann, Wilderich; Tien Zung, Nguyen. 2020. "Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19" Biology 9, no. 12: 477. https://doi.org/10.3390/biology9120477

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