Likelihood-based estimation and prediction for a measles outbreak in Samoa.

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistical Modeling

Background:

• Accurate prediction of infectious disease outbreaks is crucial for effective public health responses.
• Traditional differential equation models face challenges in parameterization and can be prone to misspecification, leading to biased predictions.
• Stochastic models offer improvements for misspecification but are computationally intensive for simulation and inference.

Purpose of the Study:

• To develop a novel, likelihood-based variation of the generalized profiling method for prediction and inference under model misspecification.
• To enable identifiability analysis and uncertainty quantification using profile likelihood methods without marginalization.
• To provide a new interpretation of model approximation as a stochastic constraint, linking profiling to stochastic models.

Main Methods:

• Development of an explicitly likelihood-based generalized profiling method.
• Application of profile likelihood for identifiability analysis and uncertainty quantification.
• Interpretation of model approximation as a stochastic constraint.

Main Results:

• The method demonstrated fast and accurate predictions during a measles outbreak in Samoa (2019-2020).
• The approach successfully performed prediction and inference under model misspecification.
• Validation and refinement of the method with additional data from the Samoa measles outbreak.

Conclusions:

• The developed generalized profiling method offers a robust tool for infectious disease outbreak prediction and inference.
• This approach effectively handles model misspecification and provides reliable uncertainty quantification.
• The method's efficiency and accuracy were confirmed through real-world application during a measles epidemic.