Bayesian Analysis and Model Discrimination in Structured Epidemic Dynamics: Estimation and Identifiability of Mixing Mechanisms Using Temporal Observations

This study presents Bayesian analysis and discrimination for the structured two levels of mixing stochastic susceptible–infective–removed (SIR) epidemic model of infectious disease spread in a closed population, given temporal epidemic data. We focus on estimating key parameters, the global and local transmission rates (βG and βL), with a view to understanding their influence on disease dynamics. Utilizing Bayesian inference, we derive the joint posterior distribution of these parameters for both complete and incomplete outbreak data scenarios. In addition, we establish a simulation-based method for discriminating between the two levels of mixing SIR models from other stochastic models and evaluate its performance through simulation experiments. Our methodologies provide valuable insights into disease transmission dynamics within and between households and can be extended to more complex models.