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  1. Article ; Online: Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model

    Michael Barfield / Maia Martcheva / Necibe Tuncer / Robert D. Holt

    Journal of Biological Dynamics, Vol 12, Iss 1, Pp 51-

    2018  Volume 88

    Abstract: This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the ...

    Abstract This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models.
    Keywords backward bifurcation ; multi-scale models ; oscillations ; immuno-eco-epi model ; stress-induced competition ; infectious disease ecology ; Environmental sciences ; GE1-350 ; Biology (General) ; QH301-705.5
    Subject code 612
    Language English
    Publishing date 2018-01-01T00:00:00Z
    Publisher Taylor & Francis Group
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Article ; Online: Dynamics of low and high pathogenic avian influenza in wild and domestic bird populations

    Necibe Tuncer / Juan Torres / Maia Martcheva / Michael Barfield / Robert D. Holt

    Journal of Biological Dynamics, Vol 10, Iss 1, Pp 104-

    2016  Volume 139

    Abstract: This paper introduces a time-since-recovery structured, multi-strain, multi-population model of avian influenza. Influenza A viruses infect many species of wild and domestic birds and are classified into two groups based on their ability to cause disease: ...

    Abstract This paper introduces a time-since-recovery structured, multi-strain, multi-population model of avian influenza. Influenza A viruses infect many species of wild and domestic birds and are classified into two groups based on their ability to cause disease: low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). Prior infection with LPAI provides partial immunity towards HPAI. The model introduced in this paper structures LPAI-recovered birds (wild and domestic) with time-since-recovery and includes cross-immunity towards HPAI that can fade with time. The model has a unique disease-free equilibrium (DFE), unique LPAI-only and HPAI-only equilibria and at least one coexistence equilibrium. We compute the reproduction numbers of LPAI ( $ {\mathcal R}_{\rm L} $ ) and HPAI ( $ {\mathcal R}_{\rm H} $ ) and show that the DFE is locally asymptotically stable when $ {\mathcal R}_{\rm L} <1 $ and $ {\mathcal R}_{\rm H} <1 $ . A unique LPAI-only (HPAI-only) equilibrium exists when $ {\mathcal R}_{\rm L} >1 $ ( $ {\mathcal R}_{\rm H} >1 $ ) and it is locally asymptotically stable if HPAI (LPAI) cannot invade the equilibrium, that is, if the invasion number $ \hat {\mathcal {R}}_{\rm L}^{\rm H} <1 $ ( $ \hat {\mathcal {R}}_{\rm H}^{\rm L} <1 $ ). We show using numerical simulations that the ODE version of the model, which is obtained by discarding the time-since-recovery structures (making cross-immunity constant), can exhibit oscillations, and also that the pathogens LPAI and HPAI can coexist with sustained oscillations in both populations. Through simulations, we show that even if both populations (wild and domestic) are sinks when alone, LPAI and HPAI can persist in both populations combined. Thus, reducing the reproduction numbers of LPAI and HPAI in each population to below unity is not enough to eradicate the disease. The pathogens can continue to coexist in both populations unless transmission between the populations is reduced.
    Keywords Mathematical models ; age-structured differential equations ; reproduction number ; invasion number ; LPAI ; HPAI ; H5N1 ; avian influenza ; Environmental sciences ; GE1-350 ; Biology (General) ; QH301-705.5
    Subject code 512
    Language English
    Publishing date 2016-01-01T00:00:00Z
    Publisher Taylor & Francis Group
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Article: Quantifying dilution and amplification in a community of hosts for tick‐borne pathogens

    Levi, Taal / Felicia Keesing / Robert D. Holt / Michael Barfield / Richard S. Ostfeld

    Ecological applications. 2016 Mar., v. 26, no. 2

    2016  

    Abstract: Recent controversy over whether biodiversity reduces disease risk (dilution effect) has focused on the ecology of Lyme disease, a tick‐borne zoonosis. A criticism of the dilution effect is that increasing host species richness might amplify disease ... ...

    Abstract Recent controversy over whether biodiversity reduces disease risk (dilution effect) has focused on the ecology of Lyme disease, a tick‐borne zoonosis. A criticism of the dilution effect is that increasing host species richness might amplify disease risk, assuming that total host abundance, and therefore feeding opportunities for ticks, increase with species richness. In contrast, a dilution effect is expected when poor quality hosts for ticks and pathogens (dilution hosts) divert tick blood meals away from competent hosts. Even if host densities are additive, the relationship between host density and tick encounters can be nonlinear if the number of ticks that encounter a host is a saturating function of host density, which occurs if ticks aggregate on the remaining hosts rather than failing to find a host before death. Both dilution and amplification are theoretical possibilities, and assessing which is more prevalent required detailed analyses of empirical systems. We used field data to explore the degree of tick redistribution onto fewer individuals with variation in intraspecific host density and novel data‐driven models for tick dynamics to determine how changes in vertebrate community composition influence the density of nymphs infected with the Lyme bacterium. To be conservative, we allowed total host density to increase additively with species richness. Our long‐term field studies found that larval and nymphal ticks redistribute onto fewer individuals as host densities decline, that a large proportion of nymphs and adults find hosts, and that mice and chipmunks feed a large proportion of nymphs. White‐footed mice, eastern chipmunks, short‐tailed shrews, and masked shrews were important amplification hosts that greatly increased the density of infected nymphs. Gray squirrels and Virginia opossums were important dilution hosts. Removing these two species increased the maximum number of larvae attached to amplification hosts by 57%. Raccoons and birds were minor dilution hosts under some conditions. Even under the assumption of additive community assembly, some species are likely to reduce the density of infected nymphs as diversity increases. If the assumption of additivity is relaxed, then species that reduce the density of small mammals through predation or competition might substantially reduce disease risk.
    Keywords Didelphis virginiana ; Lyme disease ; Peromyscus leucopus ; Procyon lotor ; Sciurus carolinensis ; Tamias striatus ; adults ; bacteria ; birds ; blood meal ; community structure ; death ; field experimentation ; hosts ; intraspecific variation ; larvae ; mice ; models ; nymphs ; pathogens ; predation ; risk ; shrews ; small mammals ; species diversity ; ticks ; zoonoses
    Language English
    Dates of publication 2016-03
    Size p. 484-498.
    Publishing place John Wiley & Sons, Ltd
    Document type Article
    Note JOURNAL ARTICLE
    ZDB-ID 1074505-1
    ISSN 1939-5582 ; 1051-0761
    ISSN (online) 1939-5582
    ISSN 1051-0761
    DOI 10.1890/15-0122
    Database NAL-Catalogue (AGRICOLA)

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  4. Article: Quantifying dilution and amplification in a community of hosts for tick‐borne pathogens

    Levi, Taal / Felicia Keesing / Robert D. Holt / Michael Barfield / Richard S. Ostfeld

    Ecological applications

    Volume v. 26,, Issue no. 2

    Abstract: Recent controversy over whether biodiversity reduces disease risk (dilution effect) has focused on the ecology of Lyme disease, a tick‐borne zoonosis. A criticism of the dilution effect is that increasing host species richness might amplify disease ... ...

    Abstract Recent controversy over whether biodiversity reduces disease risk (dilution effect) has focused on the ecology of Lyme disease, a tick‐borne zoonosis. A criticism of the dilution effect is that increasing host species richness might amplify disease risk, assuming that total host abundance, and therefore feeding opportunities for ticks, increase with species richness. In contrast, a dilution effect is expected when poor quality hosts for ticks and pathogens (dilution hosts) divert tick blood meals away from competent hosts. Even if host densities are additive, the relationship between host density and tick encounters can be nonlinear if the number of ticks that encounter a host is a saturating function of host density, which occurs if ticks aggregate on the remaining hosts rather than failing to find a host before death. Both dilution and amplification are theoretical possibilities, and assessing which is more prevalent required detailed analyses of empirical systems. We used field data to explore the degree of tick redistribution onto fewer individuals with variation in intraspecific host density and novel data‐driven models for tick dynamics to determine how changes in vertebrate community composition influence the density of nymphs infected with the Lyme bacterium. To be conservative, we allowed total host density to increase additively with species richness. Our long‐term field studies found that larval and nymphal ticks redistribute onto fewer individuals as host densities decline, that a large proportion of nymphs and adults find hosts, and that mice and chipmunks feed a large proportion of nymphs. White‐footed mice, eastern chipmunks, short‐tailed shrews, and masked shrews were important amplification hosts that greatly increased the density of infected nymphs. Gray squirrels and Virginia opossums were important dilution hosts. Removing these two species increased the maximum number of larvae attached to amplification hosts by 57%. Raccoons and birds were minor dilution hosts under some conditions. Even under the assumption of additive community assembly, some species are likely to reduce the density of infected nymphs as diversity increases. If the assumption of additivity is relaxed, then species that reduce the density of small mammals through predation or competition might substantially reduce disease risk.
    Language English
    Document type Article
    ISSN 1051-0761
    Database AGRIS - International Information System for the Agricultural Sciences and Technology

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    Order via subito

    This service is chargeable due to the Delivery terms set by subito. Orders including an article and supplementary material will be classified as separate orders. In these cases, fees will be demanded for each order.

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

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