Bayesian inference for nonlinear stochastic SIR epidemic model

ABSTRACT

Inference for epidemic parameters can be challenging, in part due to data that are intrinsically stochastic and tend to be observed by means of discrete-time sampling, which are limited in their completeness. The problem is particularly acute when the likelihood of the data is computationally intractable. Consequently, standard statistical techniques can become too complicated to implement effectively. In this work, we develop a powerful method for Bayesian paradigm for susceptible–infected–removed stochastic epidemic models via data-augmented Markov Chain Monte Carlo. This technique samples all missing values as well as the model parameters, where the missing values and parameters are treated as random variables. These routines are based on the approximation of the discrete-time epidemic by diffusion process. We illustrate our techniques using simulated epidemics and finally we apply them to the real data of Eyam plague.

KEYWORDS:

• Epidemic model
• diffusion process
• conjugate distribution
• MCMC simulation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 92D30
• 60J28
• 60J20
• 60H10
• 62F20

Acknowledgments

The authors are grateful to the referees for their constructive comments and suggestions which have greatly improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hamid El Maroufy http://orcid.org/0000-0001-8707-339X