Freedman, Isaac Gilbert
(2015)
Modeling epidemics on networks of connected communities.
Undergraduate Thesis, University of Pittsburgh.
(Unpublished)
Abstract
Advances in the fields of mathematics, physics, epidemiology, and computing have led to an incredibly productive period of epidemic modeling. Here I will present the findings of several computational studies aimed at understanding how epidemics spread across networks. I investigate specifically how epidemics spread across networks consisting of two weakly connected sub-networks (communities) with varying internal connectivities, vaccination probabilities, and probabilities of social distancing. I find that, on average, epidemics may spread across communities even for a single cross connection, that crossing over is characterized by multiple time delayed epidemic waves that result in increased epidemic duration. I develop a novel mathematical characterization of networks consisting of an arbitrary number of weakly connected communities and derive a relationship between the reproductive number (R_0) of an epidemic and the Mean Squared Displacement (MSD) of the epidemic, when the spread is viewed as the progression of multiple forward-biased random walkers. Finally, I propose a new compartmental Susceptible Exposed Infected Quarantined Recovered (SEIQR) model for the 2014 Ebola Virus Disease (EVD) outbreak based on differential equations. I extend this model to an immigration SEIQR (iSEIQR) model with a constant rate of immigration and demonstrate homologous behavior in the form of multiple infection waves between a dynamic single community network model with a constant immigration of possible exposed individuals and the two community models discussed elsewhere in this work. The applications of two community network models are discussed, especially in the context of understanding and mitigating regional and transnational epidemic spread. Pharmaceutical and non-pharmaceutical interventions, such as targeted vaccination, public health education (i.e. avoidance), quarantine, and travel restrictions are explored and some mathematical and physical applications of modeling weakly coupled sub-networks are described. Finally, several possible extensions to this work are listed and discussed.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
23 April 2015 |
| Date Type: |
Publication |
| Defense Date: |
9 April 2015 |
| Approval Date: |
23 April 2015 |
| Submission Date: |
19 April 2015 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
97 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
David C. Frederick Honors College
Dietrich School of Arts and Sciences > Physics |
| Degree: |
BPhil - Bachelor of Philosophy |
| Thesis Type: |
Undergraduate Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Random Network, Scale-Free Network, Influenza, Healthcare Disparity |
| Date Deposited: |
23 Apr 2015 17:34 |
| Last Modified: |
15 Nov 2016 14:27 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/24976 |
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