  Earlier studies have shown that, in a two component model of the universe
with dark matter and the running vacuum energy which is phenomenologically a
combination of $H^2$ and $\dot{H},$ produces either eternal deceleration or
acceleration in the absence of a bare constant in the density of the running
vacuum. In this paper we have shown that, in the interaction scenario, where
the interaction between matter and vacuum is introduced through a
phenomenological term, the two component model is capable of causing a
transition from a prior decelerated to a later accelerated epoch without a bare
constant in the running vacuum density. On contrasting the model with the
cosmological data, we have found that the interaction coupling constant, is
small enough, for a slow decay of the running vacuum. The model is subjected to
dynamical system analysis which revealed that the end de Sitter phase of the
model is a stable one. We did an analysis on the thermal behavior of the
system, which shows that the entropy is bounded at the end stage so that the
system is behaving like an ordinary macroscopic system. Apart from these we
have also performed the state finder diagnostic analysis which implies the
quintessence nature of running vacuum and confirms that the model will approach
the standard $\Lambda$CDM in the future.
