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
Summary
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.
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.
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