Microbial virus epidemics in the presence of contact-mediated host dormancy

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&al. (2015) for an archaeal host, while Jackson-Fineran (2019) and Meeske&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, 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 underlying dynamical system. That is an extension of a dynamical system considered by Beretta-Kuang (1998), known to exhibit a Hopf bifurcation, giving rise to a ‘paradox of enrichment’. We verify that the additional dormancy component can, for certain parameter ranges, prevent the associated loss of stability. Moreover, the presence of contact-mediated dormancy enables the host population to attain higher equilibrium sizes - and still avoid a persistent epidemic - than hosts without this trait.