  In this paper we propose a novel SEIR stochastic epidemic model. A
distinguishing feature of this new model is that it allows us to consider a set
up under general latency and infectious period distributions. To some extent,
queuing systems with infinitely many servers and a Markov chain with
time-varying transition rate are the very technical underpinning of the paper.
Although more general, the Markov chain is as tractable as previous models for
exponentially distributed latency and infection periods. It is also
significantly simpler and more tractable than semi-Markov models with a similar
level of generality. Based on the notion of stochastic stability, we derive a
sufficient condition for a shrinking epidemic in terms of the queuing system's
occupation rate that drives the dynamics. Relying on this condition, we propose
a class of ad-hoc stabilising mitigation strategies that seek to keep a
balanced occupation rate after a prescribed mitigation-free period. We validate
the approach in the light of recent data on the COVID-19 epidemic and assess
the effect of different stabilising strategies. The results suggest that it is
possible to curb the epidemic with various occupation rate levels, as long as
the mitigation is not excessively procrastinated.
