  The H.E.S.S. collaboration revealed the presence of a very high energy (VHE)
diffuse emission in the inner 100pc of the Galaxy in close correlation with the
Central Molecular Zone (CMZ). Recently, they deduced from this emission a
cosmic-ray (CR) over-density in the region with a local peak toward the
Galactic Center (GC) and proposed a diffusive scenario with a stationary source
at the GC to explain it. However, the high supernovae (SN) rate in the GC must
also create a sustained CR injection in the region via the shocks produced at
the time of their explosion. Considering typical diffusion coefficient close
the interstellar medium (ISM) value yields to a diffuse escape time much lower
than the recurrence time between each SN explosion, showing that a steady state
model will fail to reproduce the data. This work aims to study the impact of
the spatial and temporal distribution of SNs in the CMZ on the VHE emission
morphology and spectrum: we build a 3D model of VHE CR injection and diffusive
propagation with a realistic gas distribution. We show that a peaked gamma-ray
profile towards the GC can be obtained using realistic SN spatial distribution
taking into account the central massive star cluster. We conclude that the
contribution of SNs can not be neglected, in particular at large longitudes,
however an additional CR injection at the GC is required to reproduce the very
central excess.
