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Full text release has been delayed at the author's request until August 03, 2025

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Enhancing Spatiotemporal PDE-based Epidemic Model Analysis using Advanced Computational Techniques

David, Deepak Antony
http://orcid.org/0009-0005-6642-816X
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721208918823543

Abstract Details

2024, MS, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
The COVID-19 pandemic highlighted the need for improved and precise prediction of the spatiotemporal trends of epidemic transmission. An optimized epidemic model is crucial for effectively forecasting flow of infection. By optimizing the model parameters, they can provide valuable insights into the dynamics of infection transmission and this degree of tuning helps health officials and policymakers to make data-driven decisions regarding disease control strategies, allocation of resources, and planning for healthcare. Therefore, it highlights the need of implementing reliable optimizing strategies in case of epidemic models. Similarly, the basic and effective reproductive numbers (R0, Re) are quantitative metrics widely used for estimating the rate at which the infection propagates. The limitations of existing techniques for estimating R0 and Re points the need for novel approaches to accurately estimate them using the available data. This initial part of this study presents the development of a custom GA which is capable of efficiently searching for the parameters of an epidemic model in any specified geographical region and time period. Following this, a novel computational framework for predicting the reproduction numbers from true infection data has been presented. The computational framework is derived from a reaction-diffusion based PDE epidemic model which involves fundamental mathematical derivations for obtaining their values. The PDE model is optimized using the proposed GA and the model output using the optimized parameters is found to be in correspondence with the ground truth COVID-19 data of Hamilton county, Ohio. Subsequently, the established framework for calculating the reproduction numbers was applied on the optimized model and their predictions are found to correlate with the true incidence data. In addition, these predictions are compared with a commonly used retrospective method (Wallinga-Teunis) and are found to be in harmony thereby establishing a validation of our model and at the same time indicating its potential usage in future epidemics. In the subsequent phase of the research, we employ a LSTM network for forecasting time-varying parameters of the PDE-based compartmental model. The predictive efficacy of the model depends on accurately estimating and updating time-varying model parameters, based on true infection data. Investigating the role of deep learning methods is important in this context and remains a motivation factor. We first note that numerical data used in this work correspond to the true COVID-19 dataset of Ohio, USA. The LSTM is subject to an iterative training process for a total period of 30 days such that model parameters are generated for each day. Each iteration generates parameter values corresponding to a specific day and therefore yields a comprehensive representation of the temporal dynamics of the infection progression. Using the day-to-day infection parameters yielded by the LSTM as input to the PDE model, a forecast of infection spread is obtained from the latter and validated against empirical COVID-19 spread data. In summary, by combining advanced deep learning techniques with epidemiological modeling, this study advances both our understanding of the complex, time-varying dynamics of epidemics and our ability to accurately forecast the dynamics from available empirical data.
Manish Kumar, Ph.D. (Committee Chair)
Subramanian Ramakrishnan, Ph.D. (Committee Member)
Shelley Ehrlich, M.D. (Committee Member)
Derek Wolf, Ph.D. (Committee Member)
77 p.
Mechanical Engineering
Epidemic Modeling; Partial Differential Equations; Numerical Optimization; Numerical Analysis; Pattern Recognition; LSTM

Recommended Citations

Citations

  • David, D. A. (2024). Enhancing Spatiotemporal PDE-based Epidemic Model Analysis using Advanced Computational Techniques [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721208918823543

    APA Style (7th edition)

  • David, Deepak Antony. Enhancing Spatiotemporal PDE-based Epidemic Model Analysis using Advanced Computational Techniques. 2024. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721208918823543.

    MLA Style (8th edition)

  • David, Deepak Antony. "Enhancing Spatiotemporal PDE-based Epidemic Model Analysis using Advanced Computational Techniques." Master's thesis, University of Cincinnati, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721208918823543

    Chicago Manual of Style (17th edition)

ucin1721208918823543
© 2024, some rights reserved.Creative Commons License Enhancing Spatiotemporal PDE-based Epidemic Model Analysis using Advanced Computational Techniques by Deepak Antony David is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.