  Background: A deterministic model is developed for the spatial spread of an
epidemic disease in a geographical setting. The disease is borne by vectors to
susceptible hosts through criss-cross dynamics. The model is focused on an
epidemic outbreak that initiates from a small number of cases in a small
sub-region of the geographical setting. Methods: Partial differential equations
are formulated to describe the interaction of the model compartments. Results:
The partial differential equations of the model are analyzed and proven to be
well-posed. The epidemic outcomes of the model are correlated to the spatially
dependent parameters and initial conditions of the model. Conclusions: A
version of the model is applied to the 2015-2016 Zika outbreak in the Rio de
Janeiro Municipality in Brazil.
