Spatially-heterogeneous embedded stochastic SEIR models for the 2014-2016 Ebola outbreak in West Africa.

The dynamics of human infectious diseases are challenging to understand, particularly when a pathogen spreads spatially over a large region. We present a stochastic, spatially-heterogeneous model framework derived from the foundational SEIR compartmental model. These models utilize a graph structure of spatial locations, facilitating mobility via random walks while progressing through disease states, parameterized by the net probability flux between locations. The analysis is bolstered by Approximate Bayesian Computation, by which epidemiological and mobility parameter distributions are estimated, including an empirically adjusted reproductive number, while model structure proposals are compared using Bayes Factors. The utility of this novel class of models is demonstrated through application to the 2014-2016 Ebola outbreak in West Africa. The flexibility of such models, whose complexity may be adjusted as desired, and complementary methods of analysis enable the exploration of various spatial divisions and mobility schema, while maintaining the essential spatiotemporal disease dynamics.