We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a dormancy-based defence mechanism was described in Bautista et al (2015). We first analyse the effect of the dormancy-related model parameters on the probability of invasion of a newly arriving virus into a resident host population. It turns out that the probability of dormancy initiation upon virus contact plays a crucial role, while the lengths of the dormancy periods or the death rate during dormancy are largely irrelevant. Given successful invasion, we then show that the emergence of a persistent virus infection (epidemic) in the host population corresponds to the existence of a coexistence equilibrium for the deterministic many-particle limit of our model. In this context, all dormancy-related parameters have a significant impact. Indeed, while related systems without dormancy may exhibit a Hopf bifurcation, giving rise to a variant of the paradox of enrichment, we argue that the inclusion of dormancy can prevent this loss of stability. Finally, we show that the presence of contact-mediated dormancy enables the host population to maintain higher equilibrium sizes (resp. fitness values) - while still being able to avoid a persistent epidemic - than host populations without this trait, for which high fitness values would imply a high risk for the emergence of a persistent epidemic. This adds a twist to the relevance of reproductive trade-offs usually associated with costly dormancy traits.
Download