A Polya Urn Stochastic Model for the Analysis and Control of Epidemics on Networks
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Authors
Hayhoe, Mikhail
Date
Type
thesis
Language
eng
Keyword
Epidemics , Networks , Polya Urn Model , Control of Networks , Optimization , Stochastic Processes
Alternative Title
Abstract
This thesis introduces a model for epidemics on networks based on the classical Polya process. Temporal contagion processes are generated on the network nodes using a modified Polya sampling scheme that accounts for spatial infection among neigh- bouring nodes. The stochastic properties and asymptotic behaviour of the resulting network Polya contagion process are analyzed. Given the complicated nature of this process, three classical Polya processes, one computational and two analytical, are proposed to statistically approximate the contagion process of each node, demon- strating a good fit for a range of system parameters. An optimal control problem is formulated for minimizing the average infection using a limited curing budget, and a number of different curing strategies are presented, including a proven conver- gent gradient descent algorithm. The feasibility of the problem is proven under high curing budgets by deriving conservative lower bounds that turn some processes into supermartingales. Extensive simulations run on large-scale networks demonstrate the effectiveness of our proposed strategies.
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License
Attribution-NonCommercial 3.0 United States
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.