  This work is a series of two articles. The main goal is to rigorously derive
the degenerate parabolic-elliptic Keller-Segel system in the sub-critical
regime from a moderately interacting stochastic particle system. In the first
article [7], we establish the classical solution theory of the degenerate
parabolic-elliptic Keller-Segel system and its non-local version. In the second
article, which is the current one, we derive a propagation of chaos result,
where the classical solution theory obtained in the first article is used to
derive required estimates for the particle system. Due to the degeneracy of the
non-linear diffusion and the singular aggregation effect in the system, we
perform an approximation of the stochastic particle system by using a cut-offed
interacting potential. An additional linear diffusion on the particle level is
used as a parabolic regularization of the system. We present the propagation of
chaos result with logarithmic scalings. Consequently, the propagation of chaos
follows directly from convergence in the sense of expectation and the vanishing
viscosity argument of the Keller-Segel system.
