  ZrTe$_5$ is considered a potential candidate for either a Dirac semimetal or
a topological insulator in close proximity to a topological phase transition.
Recent optical conductivity results motivated a two-band model with a conical
dispersion in 2D, in contrast to density functional theory calculations. Here,
we reconcile the two by deriving a four-band model for ZrTe$_5$ using
$\textbf{k} \cdot \textbf{p}$ theory, and fitting its parameters to the
ab-initio band structure. The optical conductivity with an adjusted electronic
structure matches the key features of experimental data. The chemical potential
varies strongly with temperature, to the point that it may cross the gap
entirely between zero and room temperature. The temperature-dependent
resistivity displays a broad peak, and confirms theoretically the conclusions
of recent experiments attributing the origin of the resistivity peak to the
large shift of the chemical potential with temperature.
