Inference of epidemiological parameters from household stratified data

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Statistics

Background:

• Understanding disease transmission dynamics within households is crucial for effective public health interventions.
• Stochastic SIR (Susceptible-Infectious-Recovered) models with multiple mixing levels offer a framework for studying epidemic spread.
• Inferring model parameters from early epidemic data is challenging but essential for real-time forecasting.

Purpose of the Study:

• To develop and compare two Bayesian inference methods for a continuous-time Markov chain SIR model incorporating household structures.
• To estimate key epidemiological parameters, including within-household transmission, recovery rates, and between-household transmission.
• To assess the computational efficiency and accuracy of these methods for inferring epidemic growth rates and household reproduction numbers.

Main Methods:

• Utilized a stochastic households model, a continuous-time Markov chain SIR model with two levels of mixing.
• Implemented two Bayesian Markov Chain Monte Carlo (MCMC) inference approaches: exact Bayesian inference via data augmentation and approximate Bayesian inference using a branching process likelihood approximation.
• Inferred model parameters from data on infection dates and household locations.

Main Results:

• Both developed Bayesian inference methods successfully calculated joint posterior distributions for model parameters.
• The branching process approximation demonstrated good accuracy in parameter estimation compared to exact inference.
• The approximate method showed significant computational efficiency, especially as the volume of epidemic data increased.

Conclusions:

• The stochastic households model provides a robust framework for analyzing epidemic dynamics within structured populations.
• The branching process approximation offers a computationally efficient and accurate alternative for Bayesian inference in early-stage epidemic modeling.
• These methods are valuable for estimating critical epidemiological parameters from early outbreak data, aiding public health response.