Spatial processes can be important for disease spread between populations as well as within populations.  Populations that are tightly linked spatially,  due to proximity and possibly other metrics, may have similar epidemic dynamics and, as a corollary, reproductive rates of disease spread R₀.  Thus, the spatial covariance between populations may be important to account for when estimating R₀ along with its associated uncertainty. The question remains whether models that account for spatial correlation between populations provide better estimates than those that do not.  Using a Bayesian susceptible-exposed-infected-recovered (SEIR) model, we quantified R₀ for a set of eight smallpox outbreaks in Mission communities of the Southwest United States from 1780--1781.  We compared models that considered spatial correlation between outbreaks and those that did not using information theoretic criteria.  We also incorporated prior knowledge regarding the infectious and latency periods associated with smallpox to determine how prior information affected the distribution of R₀. 
Results/Conclusions

As model complexity increased, the variability surrounding estimates of R₀ also increased, which can have widespread consequences for controlling an epidemic or understanding disease spread.  In general, the spatial Bayesian SEIR models can properly combine the uncertainty associated with spatial and temporal processes to estimate R₀ and, thus, provide a clearer understanding of epidemic dynamics.