  We investigate the macroscopic time evolution and stationary states of a mean
field generalized contact process in $\mathbb{R}^d$. The model is described by
a coupled set of nonlinear integral-differential equations. It was inspired by
a model of neurons with discrete voltages evolving by a stochastic integrate
and fire mechanism. We obtain a complete solution in the spatially uniform case
and partial solutions in the general case. The system has one or more fixed
points and also traveling wave solutions.
