Volume 27, 2023
|Page(s)||174 - 220|
|Published online||20 January 2023|
Microbial virus epidemics in the presence of contact-mediated host dormancy
1 Goethe-Universität Frankfurt,
Frankfurt am Main,
2 Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Műegyetem rkp. 3., 1111 Budapest, Hungary
3 Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13–15, 1053 Budapest, Hungary
* Corresponding author: email@example.com
Accepted: 20 December 2022
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.
Mathematics Subject Classification: 92D25 / 60J85 / 34D05 / 37G15
Key words: Dormancy / host-virus system / multi-type branching process / Hopf bifurcation / paradox of enrichment / microbial virus epidemic
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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