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This study addresses fundamental problems in estimating parameters for the SEIR epidemiological model by demonstrating that its standard formulation has parameters that are not globally identifiable, leading to unreliable estimates. The researchers developed a mathematically reparameterized version of the model that is globally identifiable and computationally stable, which consistently recovers correct parameters and avoids numerical errors that plague traditional approaches. The new formulation incorporates sensitivity equations that improve both the reliability and computational efficiency of parameter estimation.
Why it matters
Accurate parameter estimation in epidemiological models is critical for disease forecasting and public health decision-making. This work provides a rigorous mathematical foundation that could improve the reliability of predictions used to guide interventions during infectious disease outbreaks, ensuring that models produce trustworthy insights rather than misleading results from incorrect parameter values.
Understand the Science
arXiv:2607.09137v1 Announce Type: cross
Abstract: The Susceptible-Exposed-Infectious-Removed (SEIR) model is a fundamental model in epidemiology. Model parameters such as the reciprocal transmission, incubation, and infectious rates are often difficult to measure directly, and they are estimated by solving an optimisation problem aiming to minimise the difference between the observed data and the model solution. However, the parameters of the standard SEIR system are not globally identifiable, causing optimisation algorithms to frequently converge to incorrect local optima and suffer from numerical stiffness. Here we show a comprehensive structural identifiability analysis of the SEIR framework, and present a globally identifiable and computationally stable reparameterisation of the model derived via an observational system approach. We fully characterise the multiple locally identifiable parameters, and by transforming the system into a globally identifiable structure, we eliminate the non-uniqueness issues in the parameter estimation approaches. Our numerical experiments demonstrate that this reformulation significantly improves convergence frequency, avoids runtime errors caused by numerical overflow, and consistently recovers the correct parameters. Furthermore, incorporating first-order sensitivity equations into the optimiser enhances the robustness and execution speed of the estimation process. Numerically well-conditioned methods for parameter identification, together with a comprehensive understanding of the identifiability of the parameters, ensure that the model yields reliable, rigorous insights for infectious disease forecasting and theoretical epidemiology.
Source: Comprehensive identifiability analysis and reliable parameter estimation for an SEIR model