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Permanent link (DOI): https://doi.org/10.7939/R3DC71

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Two Models For Indirectly Transmitted Diseases: Cholera Open Access

Descriptions

Other title
Subject/Keyword
SIR
Cholera
Epidemiology
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Davis, William L
Supervisor and department
Wang, Hao (Mathematics and Statistical Sciences)
Examining committee member and department
Wang, Hao (Mathematics and Statistical Sciences)
Hillen, Thomas (Mathematics and Statistical Sciences)
de Vries, Gerda (Mathematics and Statistical Sciences)
Heo, Giseon (School of Dentistry and Mathematics and Statistical Sciences)
Li, Michael (Mathematics and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2012-07-05T14:38:57Z
Graduation date
2012-11
Degree
Master of Science
Degree level
Master's
Abstract
Cholera remains epidemic and endemic in the world, causing thousands of deaths annually in locations lacking adequate sanitation and water infrastructure. Yet its dynamics are still not fully understood. An indirectly transmitted infectious disease model, called an iSIR model, was recently proposed for cholera. This model includes a new incidence term for indirect transmission. The analysis of the iSIR model was preliminary and here we present a thorough stability and sensitivity analysis. We introduce a new disease model, called an iSIBP model, using the new incidence term, and including bacteriophage. Our findings highlight the importance of the relationship among the water contamination parameter and the carrying capacity and minimum infectious dose of the pathogen, relating to the partial global results for the iSIR model, and the existence of limit cycles in the iSIBP model. This thesis provides a theoretical basis for further mathematical and experimental work.
Language
English
DOI
doi:10.7939/R3DC71
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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