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Three studies on random walks and disease dynamics on networks

Vargas Bernal, Esteban
http://orcid.org/0000-0002-3194-4165
http://rave.ohiolink.edu/etdc/view?acc_num=osu1658156591819527

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Mathematics.
The projects presented in this thesis are related to disease dynamics and random walks on networks. These projects consider networks of different spatial scales. In one project, we consider vector-borne disease dynamics on discrete spatial locations connected by host movement. Specifically, we compare two commonly used modeling frameworks for host movements, the Lagrangian and the Eulerian frameworks. In the second project, we extend the widely-used community detection algorithm InfoMap to absorbing random walks. The third project is a detailed study of a sexual network among men who have sex with men (MSM) in Columbus, Ohio. In particular, this latter project involves application of the InfoMap extensions developed in project two. While the Lagrangian-Eulerian and InfoMap projects are seemingly quite different, there is a shared theme of random walks on networks that connects the different projects of the thesis. We define Lagrangian and Eulerian frameworks to be consistent if there is a graph Laplacian L (representing the movement in the Eulerian framework) such that the residence times of infectious hosts in the two frameworks match. We provide a sufficient condition for consistency in terms of the mixing matrix associated with the Lagrangian approach. We examine the two-patch case, where we observe that the basic reproduction numbers of the two frameworks can be similar even when the frameworks are not consistent. In contrast, disease quantities such as outbreak final size can be significantly different even when the two frameworks are consistent. The second project concerns the community-detection algorithm InfoMap developed by Rosvall and Bergstrom. InfoMap builds on regular Markov chains and information theory to detect tightly-knit sets of nodes of a network via the minimization of an objective function called the map function. We examine the effect of disease dynamics on community structure of a network by extending InfoMap to absorbing random walks. One of our InfoMap extensions has the desirable property that its map function converges to the map function of standard InfoMap when all of the absorption rates approach zero. We study additional properties of this extension. The third project consists of application of our InfoMap extensions to empirical data on sexual networks among MSM collected through the Network Epidemiology of Syphilis Transmission (NEST) study in Columbus, Ohio. We fit an exponential random graph model (ERGM) to the NEST data, and sample a network of the fitted ERGM for our analysis. We consider pre-exposure prophylaxis (PrEP) usage as a proxy for health-care seeking to define syphilis treatment rates. We study the effect of differential absorption rates associated with differential PrEP usage on effective community structure. We also study the effect of PrEP use on disease quantities such as probability of a large outbreak, final outbreak size, outbreak peak, infection prevalence, and outbreak duration. We establish relationships between these disease quantities and effective community structure.
Joseph Tien (Advisor)
Janet Best (Committee Member)
Adrian Lam (Committee Member)
190 p.
Epidemiology; Mathematics

Recommended Citations

Citations

  • Vargas Bernal, E. (2022). Three studies on random walks and disease dynamics on networks [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1658156591819527

    APA Style (7th edition)

  • Vargas Bernal, Esteban. Three studies on random walks and disease dynamics on networks . 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1658156591819527.

    MLA Style (8th edition)

  • Vargas Bernal, Esteban. "Three studies on random walks and disease dynamics on networks ." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1658156591819527

    Chicago Manual of Style (17th edition)

osu1658156591819527
126
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