  We investigate a stochastic individual-based model for the population
dynamics of host-virus systems where the microbial hosts may transition into a
dormant state upon contact with virions, thus evading infection. Such a
contact-mediated defence mechanism was described in Bautista et al (2015) for
an archaeal host, while Jackson and Fineran (2019) and Meeske et al (2019)
describe a related, CRISPR-Cas induced, dormancy defense of bacterial hosts to
curb phage epidemics. We first analyse the effect of the dormancy-related model
parameters on the probability and time of invasion of a newly arriving virus
into a resident host population. Given successful invasion in the stochastic
system, we then show that the emergence (with high probability) of a persistent
virus infection ('epidemic') in a large host population can be determined by
the existence of a coexistence equilibrium for the dynamical system arising as
the deterministic many-particle limit of our model. This is an extension of a
dynamical system considered by Beretta and Kuang (1998) that is known to
exhibit a Hopf bifurcation, giving rise to a 'paradox of enrichment'. In our
system, we verify that the additional dormancy component can, at least for
certain parameter ranges, prevent the associated loss of stability. Finally, we
show that the presence of contact-mediated dormancy enables the host population
to attain higher equilibrium sizes - while still being able to avoid a
persistent epidemic - than host populations without this trait.
