Blath, Jochen and Tóbiás, András (2023) Microbial virus epidemics in the presence of contact-mediated host dormancy. ESAIM-PROBABILITY AND STATISTICS, 27. pp. 174-220. ISSN 1292-8100
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Abstract
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.
Item Type: | Article |
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Additional Information: | Goethe-Universitat Frankfurt, Robert-Mayer-Stra_e 10, Frankfurt am Main, 60325, Germany Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Muegyetem rkp. 3., Budapest, 1111, Hungary Alfr_ed R_enyi Institute of Mathematics, Re_altanoda utca 13-15, Budapest, 1053, Hungary Correspondence Address: Tóbiás, A.; Goethe-Universitat Frankfurt, Robert-Mayer-Stra_e 10, Germany; email: tobias@cs.bme.hu |
Uncontrolled Keywords: | Dormancy, host-virus system, multi-type branching process, Hopf bifurcation, paradox of enrichment, microbial virus epidemic |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 28 Mar 2024 09:48 |
Last Modified: | 28 Mar 2024 09:48 |
URI: | https://real.mtak.hu/id/eprint/191180 |
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