  In this paper we give fully analytical description of the dynamics of a
collection of $N$-Frenkel excitons in high density regime dispersively coupled
to a single mode cavity field, in the presence of both exciton and cavity-field
dissipations. By using excitonic operators as q-deformed bosonic operators for
the system, we solve analytically the Liouville equation for the density
operator at zero temperature and investigate the influence of the number of
excitons and the effect of both dissipations on dynamical behavior of the
system. We use the solution of master equation to explore the dissipative
dynamics of non-classical properties such as, molecule-field entanglement,
quadrature squeezing of the field, and molecular dipole squeezing. We find that
the non-classical properties are strongly affected by the number of excitons
and also by the existence of both dissipations.
