Forecasting Development of COVID-19 Epidemic in European Union Using Entropy-Randomized Approach

Cover Page

Cite item

Full Text

Abstract

The paper is devoted to the forecasting of the COVID-19 epidemic by the novel method of randomized machine learning. This method is based on the idea of estimation of probability distributions of model parameters and noises on real data. Entropy-optimal distributions correspond to the state of maximum uncertainty which allows the resulting forecasts to be used as forecasts of the most "negative" scenario of the process under study. The resulting estimates of parameters and noises, which are probability distributions, must be generated, thus obtaining an ensemble of trajectories that considered to be analyzed by statistical methods. In this work, for the purposes of such an analysis, the mean and median trajectories over the ensemble are calculated, as well as the trajectory corresponding to the mean over distribution values of the model parameters. The proposed approach is used to predict the total number of infected people using a three-parameter logistic growth model. The conducted experiment is based on real COVID-19 epidemic data in several countries of the European Union. The main goal of the experiment is to demonstrate an entropy-randomized approach for predicting the epidemic process based on real data near the peak. The significant uncertainty contained in the available real data is modeled by an additive noise within 30%, which is used both at the training and predicting stages. To tune the hyperparameters of the model, the scheme is used to configure them according to a testing dataset with subsequent retraining of the model. It is shown that with the same datasets, the proposed approach makes it possible to predict the development of the epidemic more efficiently in comparison with the standard approach based on the least-squares method.

About the authors

Y. S Popkov

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Email: popkov@isa.ru
Vavilov Str. 44/2

Y. A Dubnov

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Email: yury.dubnov@phystech.edu
Vavilov Str. 44/2

A. Yu Popkov

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Email: apopkov@isa.ru
Vavilova Str. 44/2

References

  1. van den Driessche P. Mathematical Epidemiology / ed. by Brauer F., van den Driessche P., Wu J. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. vol. 1945. Lecture Notes in Mathematics. pp. 147–157.
  2. Kumar J., Hembram K.P.S.S. Epidemiological study of novel coronavirus (COVID-19). ArXiv. 2020. URL: http://arxiv.org/abs/2003.11376 (accessed 02.09.2021).
  3. Yang W., Zhang D., Peng L., Zhuge C., and Hong L. Rational evaluation of various epidemic models based on the COVID-19 data of China. ArXiv. 2020. URL: http://arxiv.org/abs/2003.05666 (accessed 02.09.2021).
  4. Tátrai D., Várallyay Z. COVID-19 epidemic outcome predictions based on logistic fitting and estimation of its reliability. ArXiv. 2020. URL: http://arxiv.org/abs/2003.14160 (accessed 02.09.2021).
  5. Morais A.F. Logistic approximations used to describe new outbreaks in the 2020 COVID-19 pandemic. ArXiv. 2020. URL: http://arxiv.org/abs/2003.11149 (accessed 02.09.2021).
  6. Shen C.Y. Logistic growth modelling of COVID-19 proliferation in China and its international implications. International Journal of Infectious Diseases. 2020. vol. 96. pp. 582–589. URL: https://doi.org/10.1016/j.ijid.2020.04.085 (accessed 02.09.2021).
  7. Wang P., Zheng X., Li J., Zhu B. Prediction of epidemic trends in COVID-19 with logistic model and machine learning technics. Chaos, Solitons & Fractals. 2020. vol. 139. pp. 110058. URL: https://doi.org/10.1016/j.chaos.2020.110058 (accessed 02.09.2021).
  8. Chen D.-G., Chen X., Chen J.K. Reconstructing and forecasting the COVID-19 epidemic in the United States using a 5-parameter logistic growth model. Global Health Research and Policy. 2020. vol. 5. no. 1. 25 p.
  9. Попков Ю.С., Попков А.Ю., Дубнов Ю.А. Рандомизированное машинное обучение при ограниченных наборах данных: от эмпирической вероятности к энтропийной рандомизации. М.: ЛЕНАНД, 2019.
  10. Больцман Л. О связи между вторым началом механической теории теплоты и теорией вероятностей в теоремахо тепловом равновесии. Больцман Л.Э. Избранные труды. Под ред. Шлак Л.С. М.: Наука, 1984.
  11. Jaynes E.T. Information theory and statistical mechanics. Physical review. 1957. vol. 106. no. 4. pp. 620–630.
  12. Jaynes E.T. Probability theory: the logic of science. Cambridge university press. 2003.
  13. Shannon C.E. Communication theory of secrecy systems. Bell Labs Technical Journal. 1949. vol. 28. no. 4. pp. 656–715.
  14. Verhulst P.-F. Notice sur la loi que la population suit dans son accroissement. Corresp. Math. Phys. 1838. vol. 10. pp. 113–126.
  15. Singer H.M. The COVID-19 pandemic: growth patterns, power law scaling, and saturation. Physical Biology. 2020. vol. 17. no. 5. pp. 055001.
  16. Popkov Yu.S., Dubnov Yu.A., Popkov A.Yu. Randomized machine learning: Statement, solution, applications. Intelligent Systems (IS), 2016 IEEE 8th International Conference on IEEE. 2016. pp. 27–39.
  17. Popkov Y.S., Dubnov Y.A., Popkov A.Y. Introduction to the Theory of Randomized Machine Learning. Learning Systems: From Theory to Practice / ed. by Sgurev V., Piuri V., Jotsov V. Cham: Springer International Publishing, 2018. pp. 199–220.
  18. Popkov Y.S., Dubnov Y.A., Popkov A.Y. New method of randomized forecasting using entropy-robust estimation: Application to the World population prediction. Mathematics. 2016. vol. 4. no. 1. pp. 1–16.
  19. Popkov Y.S., Volkovich Z., Dubnov Y.A., Avros R., Ravve E. Entropy 2-Soft Classification of Objects. Entropy. 2017. vol. 19. no. 4. P. 178.
  20. Dubnov Y.A. Entropy-Based Estimation in Classification Problems. Automation and Remote Control. 2019. vol. 80, pp. 502–512.
  21. Popkov Y.S., Popkov A.Y., Dubnov Y.A., Solomatine D. Entropy-Randomized Forecasting of Stochastic Dynamic Regression Models. Mathematics. 2020. No. 8. pp. 1119.
  22. Popkov A.Y. Randomized machine learning of nonlinear models with application to the prediction of the development of epidemic process. Automation and Remote Control. 2021.
  23. Dong E., Du H., Gardner L. An interactive web-based dashboard to track COVID-19 in real time. The Lancet infectious diseases. 2020. vol. 20. no. 5. pp. 533–534.
  24. COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. URL: https://github.com/CSSEGISandData/COVID-19 (accessed 02.09.2021).
  25. Golan A., Judge G., Miller D. Maximum Entropy Econometrics: Robust Estimation with Limited Data. New York : John Wiley & Sons. 1996.
  26. Golan A. Information and entropy econometrics. A review and synthesis. Foundations and trends in Econometrics. 2008. vol. 2. no. 1-2. pp. 1–145.
  27. Nocedal J., Wright S. Numerical optimization. Springer Science & Business Media. 2006.
  28. Nash S.G. Newton-type minimization via the Lanczos method. SIAM Journal on Numerical Analysis. 1984. vol.21. no. 4. pp. 770–788.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).