Approximate Bayesian computation for spatial SEIR(S) epidemic models

Abstract

Approximate Bayesia n Computation (ABC) provides an attractive approach to estimation in complex Bayesian inferential problems for which evaluation of the kernel of the posterior distribution is impossible or computationally expensive. These highly parallelizable techniques have been successfully applied to many fields, particularly in cases where more traditional approaches such as Markov chain Monte Carlo (MCMC) are impractical. In this work, we demonstrate the application of approximate Bayesian inference to spatially heterogeneous Susceptible-Exposed-Infectious-Removed (SEIR) stochastic epidemic models. These models have a tractable posterior distribution, however MCMC techniques nevertheless become computationally infeasible for moderately sized problems. We discuss the practical implementation of these techniques via the open source ABSEIR package for R. The performance of ABC relative to traditional MCMC methods in a small problem is explored under simulation, as well as in the spatially heterogeneous context of the 2014 epidemic of Chikungunya in the Americas.

Keywords: Approximate Bayesian computation; Chikungunya; Compartmental Models; Epidemics.

Figure 1

Posterior and Posterior Predictive Distributions for Infectious Count

Figure 2

Reported Cumulative Chikungunya Cases by Administrative Region and Epidemiological Week

Figure 3

Underspecified Posterior Predictive Distribution: Cases for The Dominican Republic and Colombia

Figure 4

Final Posterior Predictive Distribution: Cases for The Dominican Republic and Colombia

Figure 5

Reproductive Numbers: The Dominican Republic and Colombia

Figure 6

Reproductive Numbers: Mean National Reproductive Number Trends