This paper presents the steady-state solutions and traveling wave solutions for a
spatially distributed PDE version of the spruce budworm model. The ODE
(undistributed) model has been used in practical scenarios to model the outbreaks of
the spruce budworm in forest environments, alongside the study of concepts
involving fixed points and bifurcations in introductory differential equations
courses. This study represents the spread of an outbreak from one end of
a forest to the other. Numerical simulations are conducted using spectral
methods.