  We propose a population model for $\delta$-pulse-coupled oscillators with
sparse connectivity. The model is given as an evolution equation for the phase
density which take the form of a partial differential equation with a non-local
term. We discuss the existence and stability of stationary solutions and
exemplify our approach for integrate-and-fire-like oscillators. While for
strong couplings, the firing rate of stationary solutions diverges and
solutions disappear, small couplings allow for partially synchronous states
which emerge at a supercritical Andronov-Hopf bifurcation.
