ADVANCED MATHEMATICAL SIR MODEL APPLICATIONS IN DISEASE DYNAMICS LEVERAGING MACHINE LEARNING
Keywords:
Infectious Disease Dynamics, SIR Model, Machine Learning Integration, Parameter Estimation, Epidemiological Modeling, Public Health Interventions
Abstract
The study of infectious disease dynamics has gained paramount importance in the wake of recurrent global health crises. Mathematical models like the Susceptible-Infected-Recovered (SIR) framework have been indispensable in understanding and predicting disease spread. However, these models are limited by the accuracy of their parameter estimation processes. Recent advancements in machine learning (ML) offer transformative potential for overcoming these limitations, enabling precise and adaptive parameter estimation to enhance predictive accuracy and intervention planning.
This research integrates ML techniques with the classical SIR model to improve the estimation of key parameters: the transmission rate (β), recovery rate (γ), and Using a simulated dataset mimicking realistic epidemiological conditions, ML algorithms such as Random Forest and Gradient Boosting are employed to refine parameter estimations. The results demonstrate a marked improvement in the accuracy and reliability of disease trajectory predictions, with errors reduced by up to 20% compared to traditional methods. Furthermore, sensitivity analyses reveal critical insights into the influence of β and γ on outbreak progression.
This study highlights the potential of combining mathematical models with ML methodologies to advance infectious disease modeling, offering a robust tool for public health decision-making in a rapidly changing epidemiological landscape.
References
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Li, M. Y. (2010). Mathematics of Planet Earth 2 An Introduction to Mathematical Modeling of Infectious Diseases.
Liu, M., Liu, Y., & Liu, J. (2023). Machine Learning for Infectious Disease Risk Prediction:
Bousquet, A., Conrad, W. H., Sadat, S. O., Vardanyan, N., & Hong, Y. (2022). Deep learning forecasting using time-varying parameters of the SIRD model for Covid-19. Scientific Reports, 12(1), 1–13. https://doi.org/10.1038/s41598-022-06992-0
Dattner, I., & Huppert, A. (2018). Modern statistical tools for inference and prediction of infectious diseases using mathematical models. Statistical Methods in Medical Research, 27(7), 1927–1929. https://doi.org/10.1177/0962280217746456
Davarci, O. O., Yang, E. Y., Viguerie, A., Yankeelov, T. E., & Lorenzo, G. (2024). Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States. Engineering with Computers, 40(2), 813–837. https://doi.org/10.1007/s00366-023-01816-9
Golumbeanu, M., Yang, G. J., Camponovo, F., Stuckey, E. M., Hamon, N., Mondy, M., Rees, S., Chitnis, N., Cameron, E., & Penny, M. A. (2022). Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions. Infectious Diseases of Poverty, 11(1), 1–17. https://doi.org/10.1186/s40249-022-00981-1
Jhutty, S. S., & Hernandez-Vargas, E. A. (2022). Parameter Estimation in Hybrid Machine Learning and Mechanistic Models of Infectious Diseases. IFAC-PapersOnLine, 55(16), 178–183. https://doi.org/10.1016/j.ifacol.2022.09.020
Li, M. Y. (2010). Mathematics of Planet Earth 2 An Introduction to Mathematical Modeling of Infectious Diseases.
Liu, M., Liu, Y., & Liu, J. (2023). Machine Learning for Infectious Disease Risk Prediction: A Survey. 1–45. http://arxiv.org/abs/2308.03037
Mazumdar, J. (2012). Mathematical Modelling in Epidemiology. An Introduction to Mathematical Physiology and Biology, 4(2), 109–117. https://doi.org/10.1017/cbo9781139173278.008
Nguyen, L., Raissi, M., & Seshaiyer, P. (2022). Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction. Computational and Mathematical Biophysics, 10(1), 1–17. https://doi.org/10.1515/cmb-2022-0001
Ning, X., Guan, J., Li, X. A., Wei, Y., & Chen, F. (2023). Physics-Informed Neural Networks Integrating Compartmental Model for Analyzing COVID-19 Transmission Dynamics. Viruses, 15(8), 1–16. https://doi.org/10.3390/v15081749
Ogueda-Oliva, A. G., Martínez-Salinas, E. J., Arunachalam, V., & Seshaiyer, P. (2023). Machine Learning for Predicting the Dynamics of Infectious Diseases During Travel Through Physics Informed Neural Networks. Journal of Machine Learning for Modeling and Computing, 4(3), 17–35. https://doi.org/10.1615/jmachlearnmodelcomput.2023047213
Ouyoussef, K. I., El Karkri, J., Tine, L. M., & Aboulaich, R. (2024). Physics-informed neural networks for parameter estimation and simulation of a two-group epidemiological model. International Journal of Modeling, Simulation, and Scientific Computing, 15(3), 1–16. https://doi.org/10.1142/S1793962324500429
Prasad, R., Sagar, S. K., Parveen, S., & Dohare, R. (2022). Mathematical modeling in perspective of vector-borne viral infections: a review. Beni-Suef University Journal of Basic and Applied Sciences, 11(1). https://doi.org/10.1186/s43088-022-00282-4
Reiker, T., Golumbeanu, M., Shattock, A., Burgert, L., Smith, T. A., Filippi, S., Cameron, E., & Penny, M. A. (2021). Machine learning approaches to calibrate individual-based infectious disease models. MedRxiv, 2021.01.27.21250484. https://www.medrxiv.org/content/10.1101/2021.01.27.21250484v3%0Ahttps://www.medrxiv.org/content/10.1101/2021.01.27.21250484v3.abstract
Siettos, C. I., & Russo, L. (2013). Mathematical modeling of infectious disease dynamics. Virulence, 4(4), 295–306. https://doi.org/10.4161/viru.24041
Dattner, I., & Huppert, A. (2018). Modern statistical tools for inference and prediction of infectious diseases using mathematical models. Statistical Methods in Medical Research, 27(7), 1927–1929. https://doi.org/10.1177/0962280217746456
Davarci, O. O., Yang, E. Y., Viguerie, A., Yankeelov, T. E., & Lorenzo, G. (2024). Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States. Engineering with Computers, 40(2), 813–837. https://doi.org/10.1007/s00366-023-01816-9
Golumbeanu, M., Yang, G. J., Camponovo, F., Stuckey, E. M., Hamon, N., Mondy, M., Rees, S., Chitnis, N., Cameron, E., & Penny, M. A. (2022). Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions. Infectious Diseases of Poverty, 11(1), 1–17. https://doi.org/10.1186/s40249-022-00981-1
Jhutty, S. S., & Hernandez-Vargas, E. A. (2022). Parameter Estimation in Hybrid Machine Learning and Mechanistic Models of Infectious Diseases. IFAC-PapersOnLine, 55(16), 178–183. https://doi.org/10.1016/j.ifacol.2022.09.020
Li, M. Y. (2010). Mathematics of Planet Earth 2 An Introduction to Mathematical Modeling of Infectious Diseases.
Liu, M., Liu, Y., & Liu, J. (2023). Machine Learning for Infectious Disease Risk Prediction:
Bousquet, A., Conrad, W. H., Sadat, S. O., Vardanyan, N., & Hong, Y. (2022). Deep learning forecasting using time-varying parameters of the SIRD model for Covid-19. Scientific Reports, 12(1), 1–13. https://doi.org/10.1038/s41598-022-06992-0
Dattner, I., & Huppert, A. (2018). Modern statistical tools for inference and prediction of infectious diseases using mathematical models. Statistical Methods in Medical Research, 27(7), 1927–1929. https://doi.org/10.1177/0962280217746456
Davarci, O. O., Yang, E. Y., Viguerie, A., Yankeelov, T. E., & Lorenzo, G. (2024). Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States. Engineering with Computers, 40(2), 813–837. https://doi.org/10.1007/s00366-023-01816-9
Golumbeanu, M., Yang, G. J., Camponovo, F., Stuckey, E. M., Hamon, N., Mondy, M., Rees, S., Chitnis, N., Cameron, E., & Penny, M. A. (2022). Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions. Infectious Diseases of Poverty, 11(1), 1–17. https://doi.org/10.1186/s40249-022-00981-1
Jhutty, S. S., & Hernandez-Vargas, E. A. (2022). Parameter Estimation in Hybrid Machine Learning and Mechanistic Models of Infectious Diseases. IFAC-PapersOnLine, 55(16), 178–183. https://doi.org/10.1016/j.ifacol.2022.09.020
Li, M. Y. (2010). Mathematics of Planet Earth 2 An Introduction to Mathematical Modeling of Infectious Diseases.
Liu, M., Liu, Y., & Liu, J. (2023). Machine Learning for Infectious Disease Risk Prediction: A Survey. 1–45. http://arxiv.org/abs/2308.03037
Mazumdar, J. (2012). Mathematical Modelling in Epidemiology. An Introduction to Mathematical Physiology and Biology, 4(2), 109–117. https://doi.org/10.1017/cbo9781139173278.008
Nguyen, L., Raissi, M., & Seshaiyer, P. (2022). Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction. Computational and Mathematical Biophysics, 10(1), 1–17. https://doi.org/10.1515/cmb-2022-0001
Ning, X., Guan, J., Li, X. A., Wei, Y., & Chen, F. (2023). Physics-Informed Neural Networks Integrating Compartmental Model for Analyzing COVID-19 Transmission Dynamics. Viruses, 15(8), 1–16. https://doi.org/10.3390/v15081749
Ogueda-Oliva, A. G., Martínez-Salinas, E. J., Arunachalam, V., & Seshaiyer, P. (2023). Machine Learning for Predicting the Dynamics of Infectious Diseases During Travel Through Physics Informed Neural Networks. Journal of Machine Learning for Modeling and Computing, 4(3), 17–35. https://doi.org/10.1615/jmachlearnmodelcomput.2023047213
Ouyoussef, K. I., El Karkri, J., Tine, L. M., & Aboulaich, R. (2024). Physics-informed neural networks for parameter estimation and simulation of a two-group epidemiological model. International Journal of Modeling, Simulation, and Scientific Computing, 15(3), 1–16. https://doi.org/10.1142/S1793962324500429
Prasad, R., Sagar, S. K., Parveen, S., & Dohare, R. (2022). Mathematical modeling in perspective of vector-borne viral infections: a review. Beni-Suef University Journal of Basic and Applied Sciences, 11(1). https://doi.org/10.1186/s43088-022-00282-4
Reiker, T., Golumbeanu, M., Shattock, A., Burgert, L., Smith, T. A., Filippi, S., Cameron, E., & Penny, M. A. (2021). Machine learning approaches to calibrate individual-based infectious disease models. MedRxiv, 2021.01.27.21250484. https://www.medrxiv.org/content/10.1101/2021.01.27.21250484v3%0Ahttps://www.medrxiv.org/content/10.1101/2021.01.27.21250484v3.abstract
Siettos, C. I., & Russo, L. (2013). Mathematical modeling of infectious disease dynamics. Virulence, 4(4), 295–306. https://doi.org/10.4161/viru.24041
Published
2024-12-25
How to Cite
Lutfan Anas Zahir, & Arwinda Probowati. (2024). ADVANCED MATHEMATICAL SIR MODEL APPLICATIONS IN DISEASE DYNAMICS LEVERAGING MACHINE LEARNING. INTERNATIONAL SEMINAR, 6, 800-812. Retrieved from https://conference.unita.ac.id/index.php/conference/article/view/260
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Articles
