Description
We investigate a stochastic individual-based model for the population dynamics of host--virus systems where the microbial hosts may transition into a dormant (inactive) state upon contact with virus particles, thus evading infection. Such a contact-mediated defence mechanism has recently been observed by multiple groups of biologists in the case of some bacterial and archaeal hosts. 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. The subject of this talk is joint work with Jochen Blath.