Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A Primer for parameter uncertainty,...

Area of Science:

• Mathematical modeling
• Computational biology
• Epidemiology

Background:

• Mathematical models are crucial for understanding complex systems like disease spread.
• Accurate model calibration is essential for reliable predictions and intervention strategies.
• Existing Bayesian methods for parameter estimation can be limited by prior assumptions.

Purpose of the Study:

• To introduce and illustrate a frequentist data assimilation framework for calibrating mathematical models.
• To provide an alternative to Bayesian approaches by focusing on data error structures.
• To demonstrate the application of this framework to time series data for population growth and infectious disease dynamics.

Main Methods:

• Utilized ordinary differential equation (ODE) models for temporal progression.
• Employed a frequentist data assimilation approach for model calibration.
• Focused on modeling the error structure within time series data.

Main Results:

• The framework effectively calibrates mathematical models to time series data.
• Demonstrated parameter identifiability, uncertainty quantification, and propagation.
• Evaluated model performance and forecast accuracy using simulated and real datasets.

Conclusions:

• The proposed frequentist data assimilation framework offers a robust method for model calibration.
• This approach facilitates hypothesis testing, parameter estimation, and forecasting in biological systems.
• It provides a valuable tool for analyzing infectious disease transmission and population dynamics.