{"title":"Microbial virus epidemics in the presence of contact-mediated host dormancy","authors":"J. Blath, Andr'as T'obi'as","doi":"10.1051/ps/2022022","DOIUrl":null,"url":null,"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&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.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/ps/2022022","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 3
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&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.
期刊介绍:
The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains.
Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics.
Long papers are very welcome.
Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.