  We conduct for the first time a theoretical investigation of the mid-infrared
spectral energy distribution (SED) produced by dust heated by an active
galactic nucleus (AGN) and an extreme starburst. These models employ an
integrated modeling approach using photoionization and stellar population
synthesis models in which both the line and emergent continuum is predicted
from gas exposed to the ionizing radiation from a young starburst and an AGN.
In this work, we focus on the infrared colors from the {\it Wide-field Infrared
Survey Explorer}, predicting the dependence of the colors on the input
radiation field, the ISM conditions, the obscuring column, and the metallicity.
We find that an extreme starburst can mimic an AGN in two band mid-infrared
color cuts employed in the literature. However, the three band color cuts
employed in the literature require starbursts with extremely high ionization
parameters or gas densities . We show that the extreme mid-IR colors seen in
some blue compact dwarf galaxies are not due to metallicity but rather a
combination of high ionization parameters and high column densities. Based on
our theoretical calculations, we present a theoretical mid-infrared color cut
that will exclude even the most extreme starburst that we have modeled in this
work. The theoretical AGN demarcation region presented here can be used to
identify elusive AGN candidates for future follow-up studies with the {\it
James Webb Space Telescope (JWST)}. The full suite of simulated SEDs are
available online.
