Comparative study of Bayesian and frequentist methods for epidemic forecasting: Insights from simulated and historical data

Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares (NLS) optimization versus Bayesian inference assuming a normal likelihood and using MCMC sampling in Stan. Rather than evaluating all methodological variants, we assess forecasting performance under a shared modeling structure and error assumption. The findings apply to specific implementations of both approaches. Performance is evaluated using simulated datasets (with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> and 1.5) and historical outbreaks, including the 1918 influenza pandemic, the 1896-1897 Bombay plague epidemic, and the COVID-19 pandemic. Metrics include mean absolute error (MAE), root mean squared error (RMSE), weighted interval score (WIS), and 95% prediction interval coverage. Forecasting performance varies by epidemic phase and dataset; no method consistently dominates. The Frequentist method performs well at the peak in simulations and in the post-peak phases of real outbreaks but is less accurate pre-peak. Bayesian methods, especially those with uniform priors, offer higher predictive accuracy early in epidemics and stronger uncertainty quantification when data are sparse or noisy. Frequentist methods often yield more accurate point forecasts with lower MAE, RMSE, and WIS, though their interval estimates are less robust. We also discuss the influence of prior choice and the effects of longer forecasting horizons on convergence and computational efficiency. These findings provide practical guidance for selecting estimation strategies suited to epidemic phase and data quality, aiding forecast-based decision-making.