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Spatial spread of infectious diseases

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/10839

Spatial spread of infectious diseases

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Title: Spatial spread of infectious diseases
Author: Mora, Aaron
Advisor(s): Embid, Pedro
Committee Member(s): Toolson, Eric
Wearing, Helen
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject(s): spatial spread
infectious diseases
LC Subject(s): Communicable diseases--Epidemiology--Mathematical models
Spatial analysis (Statistics)
Degree Level: Masters
Abstract: In this thesis we do a comparative study of diffusive models with non-diffusive models, looking at the effect movements in the form of simple diffusion have on the spreading of infectious diseases. This study is undertaken within the context of the SI and SIR models, two of the most fundamental models for the propagation of infectious diseases. The diffusive SI and SIR models are supplemented with no flux boundary conditions to insure meaningful comparison of the populations predictions. In addition, we use a one dimensional spatial domain for computational simplicity. The comparison of the SI (and SIR) model with its diffusive counterpart is carried out for a broad spectrum of diffusivities. We identify their ranges of diffusivities for which the predictions of the diffusive and non-diffusive models are in good agreement. Interestingly, we discovered that in the subcritical case, the diffusive SIR model predicts an epidemic outbreak whereas the standard SIR model does not.
Graduation Date: May 2010
URI: http://hdl.handle.net/1928/10839

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