  Mutations sometimes increase contagiousness for evolving pathogens. During an
epidemic, scientists use viral genome data to infer a shared evolutionary
history and connect this history to geographic spread. We propose a model that
directly relates a pathogen's evolution to its spatial contagion dynamics --
effectively combining the two epidemiological paradigms of phylogenetic
inference and self-exciting process modeling -- and apply this
\emph{phylogenetic Hawkes process} to a Bayesian analysis of 23,422 viral cases
from the 2014-2016 Ebola outbreak in West Africa. The proposed model is able to
detect individual viruses with significantly elevated rates of spatiotemporal
propagation for a subset of 1,610 samples that provide genome data. Finally, to
facilitate model application in big data settings, we develop massively
parallel implementations for the gradient and Hessian of the log-likelihood and
apply our high performance computing framework within an adaptively
preconditioned Hamiltonian Monte Carlo routine.
