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A Theoretical Framework for a Three-state Spatial Population model with applications

The theoretical work of this presentation is motivated by our efforts to understand spatial-temporal dynamics of biological systems whose main features can be roughly captured by three states. The general model is constructed and approximate sub-models used to help increase (eventually) our understanding of the dynamics of three-state systems. The pair approximation method is used to construct a spatial sub-model with nearest neighbor interaction. The spatially implicit mean field approximation of the three-state model is also investigated to study the dynamics of the null-model, that is the dynamics of a model without the spatial component. Dynamics of our approximation are compared with a stochastic computer simulation (based on continuous time Poisson processes) of the full model. The reliability of the pair approximation and the mean field model is discussed. The model is applied to the protection of crops against infestation and the spread of influenza in a closed environment with temporary vaccination.

Article Number:
MTBI-03-05M

Year:
2006

Authors:
Michelle Bettelheim, Columbia University
Jennifer Houle, University of Maine
Fabian Librado, University of Idaho
David Hiebeler, University of Maine
Karen R. RĂ­os-Soto, Cornell University

a_theoretical_framework_for_a_three-state_spatial_population_model_with_applications_.pdf