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Qualitative Analysis of Pathogen Dynamics within Cyclic and Time-Varying Water Networks

Ortiz Lugo, Alvaro A, Sr.
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563872208710325

Abstract Details

2019, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
A water distribution network is a system that aims to provide a safe water supply. Biological contamination of the system can occur through a breach in the pipes and several other factors, impacting the water quality. Frequently, microorganisms form biofilms, which are aggregates of microorganisms that adhere to solid surfaces through self-secreted extracellular polymeric substances, on the interior surface of pipes. The presence of typically harmless drinking water biofilms can allow harmful bacteria to persist within the distribution network, possibly degrading water quality. In this work, we improve upon a mathematical model of the dynamics of non-native bacteria within an extensive network of pipes containing drinking-water biofilms, for time-constant, periodic and aperiodic bounded flows. Using graph theory to represent the water network, we observe pump induced flow cycles and reversal of the water flowing within subnetworks. We analyze the dynamics of our model using Lyapunov and Floquet theory as well as super-solutions. For realistic water distribution systems, there exists a significant number of connections in the network, making the study of the stability of the entire network inefficient. To address this, we develop an efficient algorithm for predicting the long-time behavior of the pathogen population within the system and prove mathematically these predictions are equivalent to results from Lyapunov, Floquet, or other theories. Finally, we generalize and apply our theory to develop an efficient method for numerically solving the eigenvalue problem.
Benjamin Vaughan, Ph.D. (Committee Chair)
Donald French, Ph.D. (Committee Member)
Yanyu Xiao, Ph.D. (Committee Member)
207 p.
Applied Mathematics
Directed Graphs; Stability; General Biology; Biomathematics; Biology and other natural sciences; Biofilms

Recommended Citations

Citations

  • Ortiz Lugo, Sr., A. A. (2019). Qualitative Analysis of Pathogen Dynamics within Cyclic and Time-Varying Water Networks [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563872208710325

    APA Style (7th edition)

  • Ortiz Lugo, Sr., Alvaro. Qualitative Analysis of Pathogen Dynamics within Cyclic and Time-Varying Water Networks. 2019. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563872208710325.

    MLA Style (8th edition)

  • Ortiz Lugo, Sr., Alvaro. "Qualitative Analysis of Pathogen Dynamics within Cyclic and Time-Varying Water Networks." Doctoral dissertation, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563872208710325

    Chicago Manual of Style (17th edition)

ucin1563872208710325
181
© 2019, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.