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DTSTART;TZID=America/New_York:20160405T125000
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SUMMARY:Rebecca Borchering (UF Mathematics)
DESCRIPTION:Approximating the probability of invasion in discrete stochastic population models\nWhen an individual with a novel trait is introduced in a new environment\, we would like to understand what drives the likelihood that its lineage will persist. In deterministic population models\, whether the invasive population “succeeds” often depends on whether the parameters of the system fall in a super- or sub-critical regime.  In stochastic population models\, the parameters must be super-critical for there to be any chance of invasion\, but even in the super-critical regime\, chance alone allows for many invasive lineages to quickly go extinct.\n\nIn this talk\, we consider multiple methods for estimating the probability of invasion for a class of continuous-time (discrete-state) Markov chain models. Because these probabilities can be expressed in terms of an associated finite-dimensional set of difference equations\, an exact numerical solution is available. However\, it is not possible to directly interpret such results in terms of the parameters of the system. Therefore\, multiple approximation methods have been introduced. One approach\, known as the diffusion approximation\, results from recasting the discrete system as a continuous state-space stochastic differential equation and calculating the associated invasion probability.  Another approach ignores all non-linear interaction effects and reduces the CTMC to a continuous-time branching process for which the probability of persisting is known. Both of these have been shown to be inadequate in certain circumstances and\, following Doering et al ‘07\, we investigate a first order WKB approximation that has been shown to be effective in estimating other CTMC properties.
URL:https://biomath.math.ufl.edu/event/rebecca-borchering-uf/
LOCATION:368 Little Hall
CATEGORIES:Spring 2016
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DTSTART;TZID=America/New_York:20160412T125000
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CREATED:20200222T030918Z
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UID:1029-1460465400-1460468400@biomath.math.ufl.edu
SUMMARY:Derek Cummings (UF Biology and Emerging Pathogens Institute)
DESCRIPTION:Spatial and temporal dynamics of dengue in southeast Asia\nDengue viruses exist as four antigenically distinct serotypes DENV1-DENV4 that interact with each other in multiple immune-mediated mechanisms.  One of these mechanisms\, immune-mediated enhancement\, through which immunity derived from one serotype leads to either enhanced disease or enhanced viral replication of subsequent infections\, has been the focus of considerable study. In this presentation\, I will describe the work of our group to characterize the dynamic impact of immune enhancement\, the potential impact of this on vaccine design\, use and evaluation and the impact of immune enhancement on spatial temporal dynamics.
URL:https://biomath.math.ufl.edu/event/derek-cummings-uf/
LOCATION:368 Little Hall
CATEGORIES:Spring 2016
ATTACH;FMTTYPE=image/jpeg:https://biomath.math.ufl.edu/wp-content/uploads/sites/126/cummings_derek.jpg
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