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Biomedical

A Physics-Informed Neural Network approach for compartmental epidemiological models

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Caterina Millevoi,

Caterina Millevoi


Damiano Pasetto,

Damiano Pasetto


Massimiliano Ferronato

Massimiliano Ferronato


  Peer Reviewed

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© attribution CC-BY

  • 0

rating
486 Views

Added on

2024-12-15

Doi: https://doi.org/10.1371/journal.pcbi.1012387

Related Subjects
Anatomy
Biochemistry
Epidemiology
Genetics
Neuroscience
Psychology
Oncology
Medicine
Musculoskeletal science
Pediatrics
Pathology
Pharmacology
Physiology
Psychiatry
Primary care
Women and reproductive health

Abstract

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to vary in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and the state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the Italian COVID-19 pandemic. Our results show that the split implementation of PINNs outperforms the joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%). Finally, we illustrate that the proposed PINN-method can also be adopted to produced short-term forecasts of the dynamics of an epidemic.

Key Questions

1. What are Physics-Informed Neural Networks (PINNs) and how are they applied to epidemiological models?

PINNs are neural networks that incorporate both data and the governing equations of a physical system. In epidemiological models, they are used to estimate time-varying parameters and state variables by minimizing a loss function based on both observed data and the residuals of the model equations.

2. What are the main advantages of using PINNs for epidemiological modeling?

PINNs can simultaneously estimate multiple time-dependent parameters, infer dynamics using different types of data jointly, provide future projections, and train even with gaps or uncertainties in data quality. They offer a deterministic approach that can be more efficient than traditional Bayesian methods.

3. How does the split PINN approach differ from the joint approach?

The split approach trains the PINN in two steps: first on epidemiological data, then on model residuals. The joint approach minimizes a combined loss function on data and residuals simultaneously. The split approach often converges faster and provides more stable results.

4. How well do PINNs perform in estimating time-varying transmission rates?

PINNs can accurately estimate time-varying transmission rates, especially after initial periods of an outbreak. They perform well in both synthetic test cases and real-world scenarios, such as the Italian COVID-19 epidemic data, providing estimates comparable to established methods.

5. What are the limitations of the PINN approach in epidemiological modeling?

PINNs may struggle with estimating initial conditions and early outbreak dynamics. They also lack built-in uncertainty quantification, unlike Bayesian methods. Performance can degrade with limited or noisy data, and the approach may need adaptation for more complex compartmental models.

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ARTICLE USAGE


Article usage: Dec-2024 to May-2025
Show by month Manuscript Video Summary
2025 May 153 153
2025 April 92 92
2025 March 81 81
2025 February 67 67
2025 January 69 69
2024 December 24 24
Total 486 486
Show by month Manuscript Video Summary
2025 May 153 153
2025 April 92 92
2025 March 81 81
2025 February 67 67
2025 January 69 69
2024 December 24 24
Total 486 486
Related Subjects
Anatomy
Biochemistry
Epidemiology
Genetics
Neuroscience
Psychology
Oncology
Medicine
Musculoskeletal science
Pediatrics
Pathology
Pharmacology
Physiology
Psychiatry
Primary care
Women and reproductive health
copyright icon

© attribution CC-BY

  • 0

rating
486 Views

Added on

2024-12-15

Doi: https://doi.org/10.1371/journal.pcbi.1012387

Related Subjects
Anatomy
Biochemistry
Epidemiology
Genetics
Neuroscience
Psychology
Oncology
Medicine
Musculoskeletal science
Pediatrics
Pathology
Pharmacology
Physiology
Psychiatry
Primary care
Women and reproductive health

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