Bayesian inference for a susceptible-exposed-infected-recovered epidemic model with data augmentation

ABSTRACT

A Bayesian data-augmentation method allows estimating the parameters in a susceptible-exposed-infected-recovered (SEIR) epidemic model, which is formulated as a continuous-time Markov process and approximated by a diffusion process using the convergence of the master equation. The estimation was carried out with latent data points between every pair of observations simulated through the Euler-Maruyama scheme, which involves imputing the missing data in addition to the model parameters. The missing data and parameters are treated as random variables, and a Markov-chain Monte-Carlo algorithm updates the missing data and the parameter values. Numerical simulations show the effectiveness of the proposed Markov-chain Monte-Carlo algorithm.

KEYWORDS:

• Susceptible-exposed-infected-recovered epidemic model
• diffusion process
• generalized inverse Gaussian distribution
• Bayesian inference
• Markov-chain Monte-Carlo simulation
• data augmentation

Acknowledgments

We thank reviewers for their helpful comments. We acknowledge financial assistance from Sultan Moulay Sliman University (scientific research project: 16-2016) to Hamid El Maroufy.