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Two Models For Indirectly Transmitted Diseases: Cholera

  • Author / Creator
    Davis, William L
  • 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.

  • Subjects / Keywords
  • Graduation date
    2012-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3DC71
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Wang, Hao (Mathematics and Statistical Sciences)
  • Examining committee members and their departments
    • de Vries, Gerda (Mathematics and Statistical Sciences)
    • Hillen, Thomas (Mathematics and Statistical Sciences)
    • Wang, Hao (Mathematics and Statistical Sciences)
    • Li, Michael (Mathematics and Statistical Sciences)
    • Heo, Giseon (School of Dentistry and Mathematics and Statistical Sciences)