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

Area of Science:

• Epidemiology
• Mathematical Biology
• Biostatistics

Background:

• Realistic disease modeling often requires Susceptible-Exposed-Infected-Recovered (SEIR) models due to incubation periods.
• Simpler Susceptible-Infected-Recovered (SIR) models are frequently used for analytical tractability but lack biological realism.
• Bridging SEIR and SIR models is vital for accurate parameter estimation in population-level infectious disease studies.

Purpose of the Study:

• To investigate stochastic SEIR and SIR models.
• To demonstrate that SEIR dynamics can be approximated by a SIR model with time-dependent rates.
• To introduce a practical parameter inference methodology for fitting approximated models.

Main Methods:

• Stochastic modeling of SEIR and SIR frameworks.
• Derivation of a large-population Functional Law of Large Numbers (FLLN) limit.
• Development of a parameter inference method using Dynamic Survival Analysis (DSA).

Main Results:

• The SEIR model can be effectively approximated by a SIR model with time-varying infection and recovery rates.
• Theoretical support for the approximation was established using FLLN and concentration inequalities.
• The proposed DSA-based methodology successfully fits SIR models to SEIR-simulated data.

Conclusions:

• The approximation of SEIR models by time-dependent SIR models is mathematically sound and practically applicable.
• The Dynamic Survival Analysis framework provides an effective tool for parameter inference in infectious disease modeling.
• This work facilitates more biologically realistic and computationally tractable analyses of infectious disease dynamics.