  The work presented in this thesis is focused on the interacting supernova
remnants (iSNRs), a class of gamma-ray emitting SNR where the radiation arise
from the interaction of the SNR with a massive molecular cloud. At the moment
only 16 iSNR are known. Before this work, there was not any population study of
these sources. Here is proposed a model for the Galactic population of iSNRs
which can be used in order to predict the number of these systems in the Galaxy
and how many of these will be detectable by the next generation of {\gamma}-ray
instruments. iSNRs are of particular interest for the particle acceleration
study because these objects have been proved to be sites of acceleration of
protons up to high energies. Furthermore, high-energy $\gamma$-ray emission can
pinpoint the presence of energetic leptons or ions and help to constraint the
acceleration efficiency and maximum energy of accelerated particles The model
presented her was only achievable through the creation of a complete catalog of
{\gamma}-ray (both GeV and TeV) supernova remnants that for each supernova
remnants gives collect the physical and spectral information available in
litterature. Simulating and analyzing the synthetic population, it was found
that the Cherenkov Telescope Array (CTA) will be able to duplicate the number
of detected interacting systems in its survey of the Galactic plane.
