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osu1306860581.pdf (820.78 KB)
ETD Abstract Container
Abstract Header
Nonlinear Incidence of Waterborne Diseases
Author Info
Dunworth, Jeffrey B.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1306860581
Abstract Details
Year and Degree
2011, Master of Science, Ohio State University, Mathematics.
Abstract
Many waterborne diseases have two significant transmission pathways. These diseases can be contracted through interpersonal contact as well as through environmental water sources. Additionally, the dose response curve, the relationship between dose of pathogen in the water source and probability of infection, is often nonlinear. In this work we explore how these two factors affect disease dynamics using a dynamical systems approach. We derive a geometric condition for the existence/nonexistence of multiple equilibria. Using this condition, we examine several classes of dose response curves commonly used in epidemiology, such as the Beta-Poisson curve and the Hill Type 2 curve. Of the dose response curves, the Log-Normal and Hill Type 2 curves were found to be capable of multiple equilibria. Additionally, we numerically explored the model dynamics for a variety of parameter ranges and found periodic orbits consistent with seasonal disease patterns. By incorporating nonlinear incidence into a two transmission pathway model for realistic parameter ranges, we observe a wider variety of system behaviors than is possible for a single transmission linear dose response model. This suggests that for diseases with a significant secondary transmission pathway, incorporating nonlinear incidence may yield a more accurate picture of disease dynamics.
Committee
Joe Tien (Advisor)
Rebecca Garabed (Committee Member)
Pages
40 p.
Subject Headings
Mathematics
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Citations
Dunworth, J. B. (2011).
Nonlinear Incidence of Waterborne Diseases
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306860581
APA Style (7th edition)
Dunworth, Jeffrey.
Nonlinear Incidence of Waterborne Diseases.
2011. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1306860581.
MLA Style (8th edition)
Dunworth, Jeffrey. "Nonlinear Incidence of Waterborne Diseases." Master's thesis, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306860581
Chicago Manual of Style (17th edition)
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Document number:
osu1306860581
Download Count:
646
Copyright Info
© 2011, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.