Physics-informed machine learning for the COVID-19 pandemic: Adherence to social distancing and short-term predictions for eight countries

Abstract

Background: The analysis of COVID-19 infection data through the eye of Physics-inspired Artificial Intelligence leads to a clearer understanding of the infection dynamics and assists in predicting future evolution. The spreading of the pandemic during the first half of 2020 was curtailed to a larger or lesser extent through social distancing measures imposed by most countries. In the context of the standard Susceptible-Infected-Recovered (SIR) model, changes in social distancing enter through time-dependent infection rates.

Methods: In this work we use machine learning and the infection dynamical equations of SIR to extract from the infection data the degree of social distancing and, through it, assess the effectiveness of the imposed measures.

Results: Quantitative machine learning analysis is applied to eight countries with infection data from the first viral wave. We find as two extremes Greece and USA where the measures were successful and unsuccessful, respectively, in limiting spreading. This physics-based neural network approach is employed to the second wave of the infection, and by training the network with the new data, we extract the time-dependent infection rate and make short-term predictions with a week-long or even longer horizon. This algorithmic approach is applied to all eight countries with good short-term results. The data for Greece is analyzed in more detail from August to December 2020.

Conclusions: The model captures the essential spreading dynamics and gives useful projections for the spreading, both in the short-term but also for a more intermediate horizon, based on specific social distancing measures that are extracted directly from the data.

Author summary

This work combines machine learning techniques with mathematical models known in epidemiology, enabling the extraction of COVID-19 infection information in different countries. This approach controls the data-driven information and shows how various measures and practices in each country are directly reflected in the infection data. The use of machine learning, especially neural networks, allows the extraction of the time-dependent infection rate that drives the evolution of the pandemic in each country. Knowledge of the time-dependent infection rate allows short-term predictions with a week-long or even longer horizon.

Graphical abstract

Keywords

COVID-19 / physics-informed machine learning / SIR / time-dependent infection rate / short-term predictions

References

[1] Hufnagel L., Brockmann, D. , Geisel, T.. Forecast and control of epidemics in a globalized world. Proc. Natl. Acad. Sci. USA, 2004, 101 : 15124– 15129

[2] Baker R. E., Yang, W., Vecchi, G. A., Metcalf, C. J. E. , Grenfell, B. T.. Susceptible supply limits the role of climate in the early SARS-CoV-2 pandemic. Science, 2020, 369 : 315– 319

[3] Qiu Y., Chen, X. , Shi, W.. Impacts of social and economic factors on the transmission of coronavirus disease 2019 (COVID-19) in China. J. Popul. Econ., 2020, 33 : 1– 46

[4] Ardabili F., S. R., Mosavi M. COVID-19 outbreak prediction with machine learning. Algorithms, 2020, 13 : 249–

[5] ArdabiliS., Mosavi, A., Band, S. S. , Varkonyi-Koczy, A. R.. (2020) Coronavirus disease (COVID-19) global prediction using hybrid artificial intelligence method of ANN trained with grey wolf optimizer. In: 2020 IEEE 3rd International Conference and Workshop in Óbuda on Electrical and Power Engineering (CANDO-EPE), pp. 000251–000254

[6] Pinter G., Felde, I., Mosavi, A., Ghamisi, P. , Gloaguen, R.. COVID-19 pandemic prediction for hungary; a hybrid machine learning approach. Mathematics, 2020, 8 : 890–

[7] da Silva R. G., Ribeiro, M. H. D. M., Mariani, V. C. , Coelho, L. D. S.. Forecasting Brazilian and American COVID-19 cases based on artificial intelligence coupled with climatic exogenous variables. Chaos Solitons Fractals, 2020, 139 : 110027–

[8] Zhao S. , Chen, H.. Modeling the epidemic dynamics and control of COVID-19 outbreak in China. Quant. Biol., 2020, 8 : 11– 19

[9] AlbaniV. V. L., Velho, R. M. , Zubelli, J. P.. (2021) Estimating, monitoring, and forecasting the COVID-19 epidemics: A spatiotemporal approach applied to NYC data. Sci. Rep., 11, 9089

[10] LytrasT., Panagiotakopoulos, G. , Tsiodras, S.. (2020) Estimating the ascertainment rate of SARS-COV-2 infection in Wuhan, China: implications for management of the global outbreak. medRxiv, doi: 10.1101/2020.03.24.20042218

[11] Barmparis G. D. , Tsironis, G. P.. Estimating the infection horizon of COVID-19 in eight countries with a data-driven approach. Chaos Solitons Fractals, 2020, 135 : 109842–

[12] Kermack W. O. , McKendrick, A. G.. A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character, 1927, 115 : 700– 721

[13] AbadiAgarwal, M.S. (2015) TensorFlow: Large-scale machine learning on heterogeneous systems. arXiv, 1603.04467

[14] Keras. https://keras.io, Accessed: April 1, 2021

[15] KingmaD. , Ba, J.. (2017) Adam: a method for stochastic optimization. arXiv, 1412.6980

[16] RoserM., Ritchie, H., Ortiz-Ospina, E. , Hasell, J.. (2020) Coronavirus pandemic (COVID-19). https://ourworldindata.org/coronavirus, Accessed: April 1, 2021

[17] The code. https://github.com/georgiosdb/PINN-COVID-19, Accessed: April 1, 2021

[18] Raissi M., Perdikaris, P. , Karniadakis, G. E.. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys., 2019, 378 : 686– 707

[19] Hunter J. D.. Matplotlib: A 2D graphics environment. Comput. Sci. Eng., 2007, 9 : 90– 95

[20] Matplotlib basemap toolkit. https://matplotlib.org/basemap, Accessed: April 1, 2021

[21] Rosakis P. , Marketou, M. E.. Rethinking case fatality ratios for COVID-19 from a data-driven viewpoint. J. Infect., 2020, 81 : e162– e164

[22] Kaxiras E., Neofotistos, G. , Angelaki, E.. The first 100 days: Modeling the evolution of the COVID-19 pandemic. Chaos Solitons Fractals, 2020, 138 : 110114–

[23] Schüttler . COVID-19 predictions using a Gauss model, based on data from April 2. Physics, 2020, 2 : 197– 212

[24] Asteris G., P. G., Douvika A., M. D., Karamani J., C. E. A novel heuristic algorithm for the modeling and risk assessment of the COVID-19 pandemic phenomenon. Comput. Model. Eng. Sci., 2020, 125 : 815– 828

[25] PolyaninA.. D. and Zaitsev, V. F. (2002) Handbook of Exact Solutions of Ordinary Differential Equations, 2nd Ed., New York: Chapmand and Hall/CRC

COMPLIANCE WITH ETHICS GUIDELINES

The authors Georgios D. Barmparis and Giorgos P. Tsironis declare that they have no conflict of interest or financial conflicts to disclose. All procedures performed in studies involving animals were in accordance with the ethical standards of the institution or practice at which the studies were conducted, and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

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