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International Conference on Mathematical Biology and

Annual Meeting of The Society for Mathematical Biology,

July 27-30, 2009

University of British Columbia, Vancouver

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Program

Poster PS39A
Martha Garlick
Utah State University
Title Homogenization of large-scale movement models in ecology with application to the spread of chronic wasting disease in ungulate populations
Abstract A difficulty in using diffusion models to predict large scale population behaviors is that individuals move differently in differing habitat types. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion (in which an individual’s motility is based on local qualities of the environment as opposed to gradients) and apply it to a simplified model of the spread of chronic wasting disease in mule deer in the La Sal Mountains of Utah. Homogenization allows us to determine the impact of small scale (~10-100m) habitat variability on large scale (~10-100km) movement and interactions without solving on the small scale. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. Chronic wasting disease is a contagious, fatal neurological disease which could greatly impact deer and elk populations.
CoauthorsJames Powell, Mevin Hooten
LocationWoodward Lobby (Monday-Tuesday)