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On Parameter Identifiability in Network-Based Epidemic Models.

István Z Kiss1, Péter L Simon2,3

  • 1Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK. i.z.kiss@sussex.ac.uk.

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|January 27, 2023
PubMed
Summary
This summary is machine-generated.

Network epidemic models offer insights beyond random mixing but face analysis challenges. Mean-field models approximate these, yet parameter identifiability, especially distinguishing transmission rate from network density, remains difficult, often yielding unidentifiable parameters.

Keywords:
EpidemicsIdentifiabilityInference

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Classical epidemic models assume random mixing, limiting their applicability to real-world networks.
  • Network-based epidemic models offer more realistic representations but are often high-dimensional and analytically intractable.
  • Mean-field models, derived from network models, provide tractable approximations incorporating network properties.

Purpose of the Study:

  • To investigate parameter identifiability in network-based mean-field epidemic models using epidemic observations.
  • To explore the challenges in disentangling key epidemiological parameters, specifically transmission rate and network density.
  • To formalize and analytically describe the identifiability problem for improved model-data fitting.

Main Methods:

  • Utilized the analytical tractability of network-based mean-field models, including expressions for eigenvalues and final epidemic size.
  • Formulated parameter identifiability as solving a system of coupled equations based on observed growth rate and final epidemic size.
  • Investigated conditions for practical identifiability and analyzed parameter uniqueness.

Main Results:

  • Network-based mean-field models often result in practically unidentifiable parameters, meaning multiple parameter sets can explain the observed data.
  • Except for the simplest cases, unique determination of parameters like transmission rate and network density is not feasible.
  • Identifiability issues arise from a manifold of infinite measure, leading to ambiguity in model outputs.

Conclusions:

  • Parameter identifiability is a significant challenge in fitting network-based mean-field epidemic models to data.
  • The complexity of these models necessitates careful consideration of identifiability to avoid erroneous conclusions.
  • Analytical descriptions of identifiability problems enhance the understanding of fitting complex models to epidemic data.