A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant...

Area of Science:

• Mathematical Biology
• Computational Epidemiology
• Statistical Modeling

Background:

• Compartmental models, such as the susceptible-infectious-removed (SIR) model, are fundamental for understanding infectious disease dynamics.
• Traditional SIR models often assume time-invariant parameters, limiting their accuracy for long-term predictions due to factors like seasonality and interventions.
• Accurate estimation of both constant and time-varying parameters is crucial for reliable epidemiological forecasting.

Purpose of the Study:

• To develop and present a general Bayesian computational framework for state and parameter estimation in compartmental models.
• To specifically adapt this framework for the SIR model, enabling the estimation of both time-varying and time-invariant parameters.
• To provide a robust method for handling parameter variability in infectious disease modeling.

Main Methods:

• A Bayesian computational framework is detailed, extending previous work.
• The framework is tailored to the SIR model by augmenting the state vector to include time-varying parameters driven by artificial noise.
• Markov chain Monte Carlo (MCMC) algorithms are used for time-invariant parameters, while nested nonlinear filters estimate system states and time-varying parameters concurrently.

Main Results:

• The proposed framework successfully estimates both time-invariant and time-varying parameters within the SIR model.
• Demonstrated performance using synthetic data, validating the robustness and accuracy of the Bayesian approach.
• Applied the framework to real-world public health data from Ontario, showcasing its practical utility.

Conclusions:

• The developed Bayesian framework offers a robust solution for parameter estimation in compartmental models with time-varying dynamics.
• This approach enhances the predictive power of epidemiological models by accounting for parameter fluctuations.
• The methodology is effective for both simulated and real-world infectious disease data analysis.