How to correctly fit an SIR model to data from an SEIR model?

KhudaBukhsh, Wasiur R.; Rempała, Grzegorz A.

Abstract

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases. This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality. To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments.

Citation

KhudaBukhsh, W. R., & Rempała, G. A. (2024). How to correctly fit an SIR model to data from an SEIR model?. Mathematical Biosciences, 375, Article 109265. https://doi.org/10.1016/j.mbs.2024.109265

• Journal Article Type: Article
• Acceptance Date: Jul 26, 2024
• Online Publication Date: Jul 30, 2024
• Publication Date: 2024-09
• Deposit Date: Jul 27, 2024
• Publicly Available Date: Jul 31, 2025
• Journal: Mathematical Biosciences
• Print ISSN: 0025-5564
• Electronic ISSN: 1879-3134
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 375
• Article Number: 109265
• DOI: https://doi.org/10.1016/j.mbs.2024.109265
• Public URL: https://nottingham-repository.worktribe.com/output/37606011
• Additional Information: This article is maintained by: Elsevier; Article Title: How to correctly fit an SIR model to data from an SEIR model?; Journal Title: Mathematical Biosciences; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.mbs.2024.109265; Content Type: article; Copyright: © 2024 The Authors. Published by Elsevier Inc.