Young, Glenn
(2016)
Pathogen dynamics: modeling and analysis of competition, organization, and vaccination.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
The work presented in this thesis is motivated by questions arising about pathogen dynamics. The effects of pathogens can be observed on a variety of spatial scales, from within-host interactions with the immune system on the microscopic level, to the spread of communicable disease on the population level. We present analyses of three common pathogens on three different scales. In Chapter 2, we derive and study a system of ordinary differential equations modeling the competition for space and resources between a mammalian host's native intestinal microbiota and an invasive species of Salmonella Typhimurium. We use our model to discuss optimal invasion strategies that maximize the salmonella's likelihood of successfully displacing the microbiota for a spot on the intestinal wall. In Chapter 3, we analyze an anomalous behavior observed in which two interacting pulses of E. coli in a one-dimensional nutrient gradient will turn around move away from one another rather than combine. To this end, we derive a novel system of ordinary differential equations approximating the dynamics of the classic Keller-Segel partial differential equations model for bacterial chemotaxis, and use this approximation to make testable predictions about mechanisms driving the turn around behavior. Finally, in Chapter 4, we use a two-strain SIR-type model of rotavirus transmission to study the effects of vaccination on a population exposed to multiple endemic strains.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
3 October 2016 |
| Date Type: |
Publication |
| Defense Date: |
27 June 2016 |
| Approval Date: |
3 October 2016 |
| Submission Date: |
21 July 2016 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
135 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Mathematical biology, pathogen dynamics |
| Date Deposited: |
03 Oct 2016 22:00 |
| Last Modified: |
15 Nov 2016 14:34 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/28720 |
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