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Non-spatial and spatial models for multi-host pathogen spread in competing species : applications to barley yellow dwarf virus and rinderpest

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dc.contributor.advisor Bokil, Vrushali A.
dc.creator Manore, Carrie Anna
dc.date.accessioned 2011-06-28T21:15:36Z
dc.date.available 2011-06-28T21:15:36Z
dc.date.copyright 2011-05-31
dc.date.issued 2011-06-28
dc.identifier.uri http://hdl.handle.net/1957/21878
dc.description Graduation date: 2012 en_US
dc.description.abstract Modeling and analyzing the combined effects of disease and population dynamics is important in understanding the effects of mechanisms such as pathogen transmission and direct competition between host species on the distribution and abundance of different species in an ecological community. Mathematical analysis of such models in a spatially explicit environment gives additional important insight into these systems. Motivated by our participation in the IGERT Ecosystem Informatics program, we explore the interactions between and among disease, competition, and spatial heterogeneity from a mathematical modeling perspective. In particular, we formulate a model in which two species compete directly via Lotka-Volterra competition and share a directly transmitted pathogen via both mass action (density-dependent) and frequency-dependent incidence. We determine conditions under which the pathogen is endemic as well as conditions for long-term coexistence of the two species and the pathogen. As the interior equilibria are intractable, we examine a special case for which full stability analysis is possible. We show that in this case, mass action and frequency incidence behave qualitatively the same. We prove existence, uniqueness, and stability for the full model with frequency incidence under the assumption of no death due to disease using theory of asymptotically autonomous equations. Using persistence theory, we show that for the full model with mass action, if all boundary equilibria are unstable, then both species and the pathogen persist uniformly strongly. We extend the multi-host competition-disease model to include multiple patches in order to model Barley Yellow Dwarf Virus in native grasslands. Our results suggest that connectivity can interact with arrival time and host infection tolerance to determine the success or failure of an invasion. Lastly, we simulate the spread of the multi-host virus rinderpest in livestock across the United States, finding that the outcome varies greatly with the starting location of the epidemic. en_US
dc.language.iso en_US en_US
dc.subject Lotka-Volterra competition en_US
dc.subject patch model en_US
dc.subject disease model en_US
dc.subject Barley Yellow Dwarf Virus en_US
dc.subject rinderpest en_US
dc.subject strong uniform persistence en_US
dc.subject.lcsh Barley yellow dwarf viruses -- Mathematical models en_US
dc.subject.lcsh Plant-pathogen relationships -- Mathematical models en_US
dc.subject.lcsh Virus-vector relationships -- Mathematical models en_US
dc.subject.lcsh Grasses -- Virus diseases -- Epidemiology -- Mathematical models en_US
dc.subject.lcsh Aphids as carriers of disease -- Mathematical models en_US
dc.subject.lcsh Livestock -- Virus diseases -- Epidemiology -- Mathematical models en_US
dc.subject.lcsh Rinderpest -- Epidemiology -- Mathematical models en_US
dc.title Non-spatial and spatial models for multi-host pathogen spread in competing species : applications to barley yellow dwarf virus and rinderpest en_US
dc.type Thesis/Dissertation en_US
dc.degree.name Doctor of Philosophy (Ph. D.) in Mathematics en_US
dc.degree.level Doctoral en_US
dc.degree.discipline Science en_US
dc.degree.grantor Oregon State University en_US
dc.contributor.committeemember Rossignol, Philippe A.
dc.contributor.committeemember Ossiander, Mina E.
dc.contributor.committeemember Gibson, Nathan L.
dc.contributor.committeemember McEvoy, Peter B.
dc.contributor.committeemember Schmittner, Andreas


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