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  1. Article ; Online: Local approximation of Markov chains in time and space.

    Milliken, Evan

    Journal of biological dynamics

    2019  Volume 13, Issue sup1, Page(s) 265–287

    Abstract: In epidemic modelling, the emergence of a disease is characterized by the low numbers of infectious individuals. Environmental randomness impacts outcomes such as the outbreak or extinction of the disease in this case. This randomness can be accounted ... ...

    Abstract In epidemic modelling, the emergence of a disease is characterized by the low numbers of infectious individuals. Environmental randomness impacts outcomes such as the outbreak or extinction of the disease in this case. This randomness can be accounted for by modelling the system as a continuous time Markov chain,
    MeSH term(s) Basic Reproduction Number ; Communicable Diseases/epidemiology ; Markov Chains ; Models, Biological ; Probability ; Time Factors
    Language English
    Publishing date 2019-01-24
    Publishing country England
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S.
    ISSN 1751-3766
    ISSN (online) 1751-3766
    DOI 10.1080/17513758.2019.1569269
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Effect of Movement on the Early Phase of an Epidemic.

    Arino, Julien / Milliken, Evan

    Bulletin of mathematical biology

    2022  Volume 84, Issue 11, Page(s) 128

    Abstract: The early phase of an epidemic is characterized by a small number of infected individuals, implying that stochastic effects drive the dynamics of the disease. Mathematically, we define the stochastic phase as the time during which the number of infected ... ...

    Abstract The early phase of an epidemic is characterized by a small number of infected individuals, implying that stochastic effects drive the dynamics of the disease. Mathematically, we define the stochastic phase as the time during which the number of infected individuals remains small and positive. A continuous-time Markov chain model of a simple two-patch epidemic is presented. An algorithm for formalizing what is meant by small is presented, and the effect of movement on the duration of the early stochastic phase of an epidemic is studied.
    MeSH term(s) Epidemics ; Humans ; Markov Chains ; Mathematical Concepts ; Models, Biological ; Stochastic Processes
    Language English
    Publishing date 2022-09-23
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 184905-0
    ISSN 1522-9602 ; 0007-4985 ; 0092-8240
    ISSN (online) 1522-9602
    ISSN 0007-4985 ; 0092-8240
    DOI 10.1007/s11538-022-01077-5
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    In stock of ZB MED Cologne/Königswinter

    Zs.B 754: Show issues Location:
    Je nach Verfügbarkeit (siehe Angabe bei Bestand)
    bis Jg. 2021: Bestellungen von Artikeln über das Online-Bestellformular
    ab Jg. 2022: Lesesaal (EG)

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  3. Article ; Online: Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection.

    Arino, Julien / Milliken, Evan

    Journal of mathematical biology

    2022  Volume 84, Issue 7, Page(s) 61

    Abstract: Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals ... ...

    Abstract Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.
    MeSH term(s) COVID-19/epidemiology ; COVID-19/prevention & control ; Humans ; Markov Chains ; Models, Biological ; Vaccination ; Vaccines
    Chemical Substances Vaccines
    Language English
    Publishing date 2022-06-23
    Publishing country Germany
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 187101-8
    ISSN 1432-1416 ; 0303-6812
    ISSN (online) 1432-1416
    ISSN 0303-6812
    DOI 10.1007/s00285-022-01765-9
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    In stock of ZB MED Cologne/Königswinter

    Zs.A 1495: Show issues Location:
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    bis Jg. 1994: Bestellungen von Artikeln über das Online-Bestellformular
    Jg. 1995 - 2021: Lesesall (1.OG)
    ab Jg. 2022: Lesesaal (EG)

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  4. Article ; Online: The Probability of Extinction of Infectious Salmon Anemia Virus in One and Two Patches.

    Milliken, Evan

    Bulletin of mathematical biology

    2017  Volume 79, Issue 12, Page(s) 2887–2904

    Abstract: Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth-death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle's study of a susceptible-infected-recovered ( ... ...

    Abstract Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth-death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle's study of a susceptible-infected-recovered (SIR) model in the 1950s. In the case of an SIR model, the presence of only one infectious class allows for the use of single-type branching processes. Multitype branching processes allow for multiple infectious classes and have latterly been used to study metapopulation models of disease. In this article, we develop a continuous time Markov chain (CTMC) model of infectious salmon anemia virus in two patches, two CTMC models in one patch and companion multitype branching process (MTBP) models. The CTMC models are related to deterministic models which inform the choice of parameters. The probability of extinction is computed for the CTMC via numerical methods and approximated by the MTBP in the supercritical regime. The stochastic models are treated as toy models, and the parameter choices are made to highlight regions of the parameter space where CTMC and MTBP agree or disagree, without regard to biological significance. Partial extinction events are defined and their relevance discussed. A case is made for calculating the probability of such events, noting that MTBPs are not suitable for making these calculations.
    MeSH term(s) Animals ; Basic Reproduction Number ; Fish Diseases/epidemiology ; Fish Diseases/transmission ; Fish Diseases/virology ; Isavirus/pathogenicity ; Markov Chains ; Mathematical Concepts ; Models, Biological ; Orthomyxoviridae Infections/epidemiology ; Orthomyxoviridae Infections/veterinary ; Orthomyxoviridae Infections/virology ; Probability ; Salmon ; Stochastic Processes
    Language English
    Publishing date 2017-12
    Publishing country United States
    Document type Journal Article
    ZDB-ID 184905-0
    ISSN 1522-9602 ; 0007-4985 ; 0092-8240
    ISSN (online) 1522-9602
    ISSN 0007-4985 ; 0092-8240
    DOI 10.1007/s11538-017-0355-5
    Database MEDical Literature Analysis and Retrieval System OnLINE

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    In stock of ZB MED Cologne/Königswinter

    Zs.B 754: Show issues Location:
    Je nach Verfügbarkeit (siehe Angabe bei Bestand)
    bis Jg. 2021: Bestellungen von Artikeln über das Online-Bestellformular
    ab Jg. 2022: Lesesaal (EG)

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  5. Article ; Online: Risk of COVID-19 variant importation - How useful are travel control measures?

    Arino, Julien / Boëlle, Pierre-Yves / Milliken, Evan / Portet, Stéphanie

    Infectious Disease Modelling

    2021  Volume 6, Page(s) 875–897

    Abstract: We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to ... ...

    Abstract We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to evaluate the contribution of importations to the dynamics of the disease in a community. We find that after an initial seeding, the role of importations becomes marginal compared to that of community-based propagation. We also evaluate the role of two travel control measures, quarantine and travel interruptions. We conclude that quarantine is an efficacious way of lowering importation rates, while travel interruptions have the potential to delay the consequences of importations but need to be applied within a very tight time window following the initial emergence of the variant.
    Language English
    Publishing date 2021-07-11
    Publishing country China
    Document type Journal Article
    ZDB-ID 3015225-2
    ISSN 2468-0427 ; 2468-2152
    ISSN (online) 2468-0427
    ISSN 2468-2152
    DOI 10.1016/j.idm.2021.06.006
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  6. Article ; Online: Risk of COVID-19 variant importation - How useful are travel control measures?

    Arino, Julien / Boelle, Pierre-Yves / Milliken, Evan M / Portet, Stephanie

    medRxiv

    Abstract: We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to ... ...

    Abstract We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to evaluate the contribution of importations to the dynamics of the disease in a community. We find that after an initial seeding, the role of importations becomes marginal compared to that of community-based propagation. We also evaluate the role of two travel control measures, quarantine and travel interruptions. We conclude that quarantine is an efficacious way of lowering importation rates, while travel interruptions have the potential to delay the consequences of importations but need to be applied within a very tight time window following the initial emergence of the variant.
    Keywords covid19
    Language English
    Publishing date 2021-05-15
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2021.05.13.21257141
    Database COVID19

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