Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Statistics

Background:

• Stochastic SEIR models are crucial for analyzing epidemic data, but often assume constant removal rates.
• Real-world epidemics frequently exhibit time-dependent removal rates, challenging standard model assumptions.
• Partially observed data, with only removal times available, necessitates advanced inference techniques.

Purpose of the Study:

• To develop and validate methods for stochastic SEIR models with time-dependent step-function removal rates.
• To enable Bayesian inference on model parameters, especially those defining the step changes in removal rates.
• To assess the impact of time-dependent removal rates on epidemic process inferences.

Main Methods:

• Development of a reversible jump Markov Chain Monte Carlo (MCMC) algorithm.
• Bayesian inference framework for estimating time-dependent parameters in SEIR models.
• Application to real-world datasets from smallpox and respiratory disease outbreaks.

Main Results:

• The proposed MCMC algorithm successfully performs Bayesian inference on models with step-function removal rates.
• Analyses demonstrate the critical importance of incorporating time-dependent removal rates for accurate epidemic modeling.
• Contrasting predictive distributions revealed significant improvements when time dependence was considered.

Conclusions:

• Time-dependent removal rates are essential for accurate SEIR modeling of many epidemics.
• The developed Bayesian MCMC method provides a robust framework for inferring these time-varying parameters.
• Accurate epidemic forecasting requires models that reflect the dynamic nature of disease transmission and removal processes.