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A combined neural ODE-Bayesian optimization approach to resolve dynamics and estimate parameters for a modified SIR model with immune memory

Liu, Donglin LU and Sopasakis, Alexandros LU orcid (2024) In Heliyon 10(19).
Abstract

We propose a novel hybrid approach that integrates Neural Ordinary Differential Equations (NODEs) with Bayesian optimization to address the dynamics and parameter estimation of a modified time-delay-type Susceptible-Infected-Removed (SIR) model incorporating immune memory. This approach leverages a neural network to produce continuous multi-wave infection profiles by learning from both data and the model. The time-delay component of the SIR model, expressed through a convolutional integral, results in an integro-differential equation. To resolve these dynamics, we extend the NODE framework, employing a Runge-Kutta solver, to handle the challenging convolution integral, enabling us to fit the data and learn the parameters and dynamics of... (More)

We propose a novel hybrid approach that integrates Neural Ordinary Differential Equations (NODEs) with Bayesian optimization to address the dynamics and parameter estimation of a modified time-delay-type Susceptible-Infected-Removed (SIR) model incorporating immune memory. This approach leverages a neural network to produce continuous multi-wave infection profiles by learning from both data and the model. The time-delay component of the SIR model, expressed through a convolutional integral, results in an integro-differential equation. To resolve these dynamics, we extend the NODE framework, employing a Runge-Kutta solver, to handle the challenging convolution integral, enabling us to fit the data and learn the parameters and dynamics of the model. Additionally, through Bayesian optimization, we enhance prediction accuracy while focusing on long-term dynamics. Our model, applied to COVID-19 data from Mexico, South Africa, and South Korea, effectively learns critical time-dependent parameters and provides accurate short- and long-term predictions. This combined methodology allows for early prediction of infection peaks, offering significant lead time for public health responses.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Forecasting, Neural ordinary differential equations, Parameter estimation, SIR model, Time-delay loss of immunity
in
Heliyon
volume
10
issue
19
article number
e38276
publisher
Elsevier
external identifiers
  • pmid:39391478
  • scopus:85204797069
ISSN
2405-8440
DOI
10.1016/j.heliyon.2024.e38276
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2024 The Author(s)
id
ca325a11-a654-4aa7-b203-42556d9a8dd0
date added to LUP
2024-10-17 17:40:49
date last changed
2025-07-11 17:10:28
@article{ca325a11-a654-4aa7-b203-42556d9a8dd0,
  abstract     = {{<p>We propose a novel hybrid approach that integrates Neural Ordinary Differential Equations (NODEs) with Bayesian optimization to address the dynamics and parameter estimation of a modified time-delay-type Susceptible-Infected-Removed (SIR) model incorporating immune memory. This approach leverages a neural network to produce continuous multi-wave infection profiles by learning from both data and the model. The time-delay component of the SIR model, expressed through a convolutional integral, results in an integro-differential equation. To resolve these dynamics, we extend the NODE framework, employing a Runge-Kutta solver, to handle the challenging convolution integral, enabling us to fit the data and learn the parameters and dynamics of the model. Additionally, through Bayesian optimization, we enhance prediction accuracy while focusing on long-term dynamics. Our model, applied to COVID-19 data from Mexico, South Africa, and South Korea, effectively learns critical time-dependent parameters and provides accurate short- and long-term predictions. This combined methodology allows for early prediction of infection peaks, offering significant lead time for public health responses.</p>}},
  author       = {{Liu, Donglin and Sopasakis, Alexandros}},
  issn         = {{2405-8440}},
  keywords     = {{Forecasting; Neural ordinary differential equations; Parameter estimation; SIR model; Time-delay loss of immunity}},
  language     = {{eng}},
  month        = {{10}},
  number       = {{19}},
  publisher    = {{Elsevier}},
  series       = {{Heliyon}},
  title        = {{A combined neural ODE-Bayesian optimization approach to resolve dynamics and estimate parameters for a modified SIR model with immune memory}},
  url          = {{http://dx.doi.org/10.1016/j.heliyon.2024.e38276}},
  doi          = {{10.1016/j.heliyon.2024.e38276}},
  volume       = {{10}},
  year         = {{2024}},
}