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Identifiability in Epidemic Models with Prior Immunity and Under-Reporting.

Fanny Bergström1, Martina Favero2, Tom Britton2

  • 1Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden. fanny.bergstrom@math.su.se.

Bulletin of Mathematical Biology
|May 19, 2026
PubMed
Summary
This summary is machine-generated.

Ensuring mathematical model identifiability is crucial for infectious disease control. Combining reported cases with immunity survey data uniquely estimates key parameters, improving public health policy recommendations.

Keywords:
EpidemicsParameter unidentifiabilitySIRUnder-reporting

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Identifiability in mathematical modeling is essential for accurate parameter estimation.
  • Infectious disease models require careful identifiability analysis to avoid misleading results and unreliable policy recommendations.
  • A modified Susceptible-Infectious-Recovered (SIR) model incorporating under-reporting and prior immunity was investigated.

Purpose of the Study:

  • To mathematically prove the structural unidentifiability of a deterministic SIR model for estimating under-reporting, prior immunity, and transmission rate using only reported case data.
  • To demonstrate how incorporating additional data sources can achieve parameter identifiability.
  • To highlight the importance of identifiability analysis in infectious disease modeling for public health decision-making.

Main Methods:

  • Mathematical proof of structural unidentifiability for the deterministic SIR model.
  • Analytical and simulation-based analysis using a stochastic SIR model.
  • Comparison of parameter estimation with reported case data alone versus combined with survey data.

Main Results:

  • The deterministic SIR model is structurally unidentifiable when estimating the fraction under-reporting, prior immunity proportion, and community transmission rate solely from reported case data.
  • Parameter identifiability for all three investigated parameters is achieved when reported incidence data is supplemented with sample survey data on prior immunity or prevalence.
  • The study confirms limitations in parameter inference for partially observed epidemics.

Conclusions:

  • Identifiability analysis is critical for the valid application of infectious disease models in public health.
  • Integrating diverse data streams, such as epidemiological case reports and population immunity surveys, enhances model reliability.
  • Accurate parameter estimation is fundamental for developing effective infectious disease control strategies and policy recommendations.