Aaron Mora

Publication Date

6-25-2010

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.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Pedro Embid

Second Committee Member

Eric Craig Toolson

Third Committee Member

Helen Wearing

Language

English

Keywords

Communicable diseases--Epidemiology--Mathematical models, Spatial analysis (Statistics)

Document Type

Thesis

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