# On Data Driven SIRD Model of Delta and Omicron Variants of COVID-19

## DOI:

https://doi.org/10.5614/cbms.2024.7.1.3## Keywords:

Compartmental model, SIRD model, SINDy, Data-driven model, Covid-19 variants## Abstract

The compartmental model stands as a cornerstone in quantitatively describing the transmission dynamics of diseases. Through a series of assumptions, this model can be formulated and subsequently validated against real-world conditions. Leveraging the abundance of COVID-19 data presently available, this study endeavors to reverse engineer the model construction process. Specifically, we analyse the compartmental model governing two notable variants of COVID-19: Delta and Omicron, utilizing empirical data. Employing the SINDy method, we extract parameters that define the model by effectively fitting the available data. To ensure robustness, the obtained model undergoes validation via comparison with real-world data through numerical integration. Additionally, we conduct fine-tuning in regularization techniques and input features to refine model selection. The constructed model then undergoes thorough analysis to gain qualitative insights and interpretations regarding the transmission dynamics of COVID-19.

## References

Weiss, R. A. and McMichael, A. J., Social and environmental risk factors in the emergence of infectious diseases, Nature Medicine, 10, pp. 70-76, 2004.

Cucinotta, D. and Vanelli, M., WHO declares COVID-19 a pandemic, Acta Bio Medica: Atenei Parmensis, 91(1), p. 157-160, 2020.

Satrio, C.B.A., Darmawan, W., Nadia, B.U. and Hanafiah, N., Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET, Procedia Computer Science, 179, pp. 524-532, 2021.

ArunKumar, K.E., Kalaga, D.V., Kumar, C.M.S., Kawaji, M. and Brenza, T.M., Forecasting of COVID-19 using deep layer recurrent neural networks (RNNs) with gated recurrent units (GRUs) and long short-term memory (LSTM) cells, Chaos, Solitons & Fractals, 146, p. 110861, 2021.

Rauf, H.T., Lali, M.I.U., Khan, M.A., Kadry, S., Alolaiyan, H., Razaq, A. and Irfan, R., Time series forecasting of COVID-19 transmission in Asia Pacific countries using deep neural networks, Personal and Ubiquitous Computing, pp. 1-18, 2023.

Taj, R.M., El Mouden, Z.A., Jakimi, A. and Hajar, M., Towards using recurrent neural networks for predicting influenza-like illness: case study of covid-19 in Morocco, International Journal of Advanced Trends in Computer Science and Engineering, 9(5), 2020.

Hethcote, H.W., Three basic epidemiological models, In Applied Mathematical Ecology, pp. 119-144, 1989.

Soewono, E., On the analysis of Covid-19 transmission in Wuhan, Diamond Princess and Jakarta-cluster, Communication in Biomathematical Sciences, 3(1), pp. 9-18, 2020.

Abdy, M., Side, S., Annas, S., Nur, W. and Sanusi, W., An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia, Advances in Difference Equations, 2021, pp. 1-17, 2021.

Susanto, H., Tjahjono, V.R., Hasan, A., Kasim, M.F., Nuraini, N., Putri, E.R.M., Kusdiantara, R. and Kurniawan, H., How many can you infect? simple (and naive) methods of estimating the reproduction number, Communication in Biomathematical Sciences, 3(1), pp. 28-36, 2020.

Cooper, I., Mondal, A. and Antonopoulos, C.G., A SIR model assumption for the spread of COVID-19 in different communities, Chaos, Solitons & Fractals, 139, p. 110057, 2020.

Feng, S., Feng, Z., Ling, C., Chang, C. and Feng, Z., Prediction of the COVID-19 epidemic trends based on SEIR and AI models, PloS One, 16(1), p. e0245101, 2021.

Zisad, S.N., Hossain, M.S., Hossain, M.S. and Andersson, K., An integrated neural network and SEIR model to predict Covid-19, Algorithms, 14(3), p. 94, 2021.

Brunton, S.L., Proctor, J.L. and Kutz, J.N., Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences, 113(15), pp. 3932-3937, 2016.

Cranmer, M., Sanchez Gonzalez, A., Battaglia, P., Xu, R., Cranmer, K., Spergel, D. and Ho, S., Discovering symbolic models from deep learning with inductive biases, Advances in Neural Information Processing Systems, 33, pp. 17429-17442, 2020.

Pan, S. and Duraisamy, K., On the structure of time-delay embedding in linear models of non-linear dynamical systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(7), 2020.

Lusch, B., Kutz, J.N. and Brunton, S.L., Deep learning for universal linear embeddings of nonlinear dynamics, Nature Communications, 9(1), p. 4950, 2018.

Rudy, S., Alla, A., Brunton, S.L. and Kutz, J.N., Data-driven identification of parametric partial differential equations, SIAM Journal on Applied Dynamical Systems, 18(2), pp. 643-660, 2019.

Shea, D.E., Brunton, S.L. and Kutz, J.N., SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems, Physical Review Research, 3(2), p. 023255, 2021.

Kaiser, E., Kutz, J.N. and Brunton, S.L., Sparse identification of nonlinear dynamics for model predictive control in the low-data limit, Proceedings of the Royal Society A, 474(2219), p. 20180335, 2018.

Brunton, S.L., Brunton, B.W., Proctor, J.L., Kaiser, E. and Kutz, J.N., Chaos as an intermittently forced linear system, Nature communications, 8(1), p. 19. 2017.

Bramburger, J.J., Kutz, J.N. and Brunton, S.L., Data-driven stabilization of periodic orbits, IEEE Access, 9, pp. 43504-43521, 2021.

Mangan, N.M., Askham, T., Brunton, S.L., Kutz, J.N. and Proctor, J.L., Model selection for hybrid dynamical systems via sparse regression, Proceedings of the Royal Society A, 475(2223), p. 20180534, 2019.

Qin, H., Machine learning and serving of discrete field theories, Scientific Reports, 10(1), p. 19329, 2020.

Guan, Y., Brunton, S.L. and Novosselov, I., Sparse nonlinear models of chaotic electroconvection, Royal Society Open Science, 8(8), p. 202367, 2021.

Wang, R., Kalnay, E. and Balachandran, B., Neural machine-based forecasting of chaotic dynamics, Nonlinear Dynamics, 98(4), pp. 2903-2917, 2019.

Gin, C.R., Shea, D.E., Brunton, S.L. and Kutz, J.N., DeepGreen: deep learning of Green's functions for nonlinear boundary value problems, Scientific Reports, 11(1), p. 21614, 2021.

Brunton, S.L., Hemati, M.S. and Taira, K., Special issue on machine learning and data-driven methods in fluid dynamics, Theoretical and Computational Fluid Dynamics, 34(4), pp. 333-337, 2020.

Brunton, S.L., Noack, B.R. and Koumoutsakos, P., Machine learning for fluid mechanics, Annual Review of Fluid Mechanics, 52, pp. 477-508, 2020.

Horrocks, J. and Bauch, C.T., Algorithmic discovery of dynamic models from infectious disease data, Scientific Reports, 10(1), p. 7061, 2020.

Jiang, Y.X., Xiong, X., Zhang, S., Wang, J.X., Li, J.C. and Du, L., Modeling and prediction of the transmission dynamics of COVID-19 based on the SINDy-LM method, Nonlinear Dynamics, 105(3), pp. 2775-2794, 2021.

Ihsan, A.F., Data-driven Identification of Compartmental Model of COVID-19, In 2021 International Conference on Data Science and Its Applications (ICoDSA), IEEE, pp. 91-96, 2021.

Arlis, S. and Defit, S., Machine learning algorithms for predicting the spread of COVID-19 in Indonesia, TEM Journal, 10(2), pp. 970-974, 2021.

Mathieu, E., Ritchie, H., Rod es-Guirao, L., Appel, C., Giattino, C., Hasell, J., Macdonald, B., Dattani, S., Beltekian, D., Ortiz-Ospina, E. and Roser, M., Coronavirus pandemic (covid-19), Our World in Data, 2020. https://ourworldindata.org/coronavirus.

Zou, H. and Hastie, T., Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society Series B: Statistical Methodology, 67(2), pp. 301-320, 2005.

## Downloads

## Published

## How to Cite

*Communication in Biomathematical Sciences*,

*7*(1), 50-60. https://doi.org/10.5614/cbms.2024.7.1.3

## Issue

## Section

## License

Copyright (c) 2024 Communication in Biomathematical Sciences

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.