{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/102436"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/102436","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Virus spread over networks: Modeling, analysis, and control","abstract":"Made available in DSpace on 2019-02-06T19:36:02Z (GMT). No. of bitstreams: 2 PARE-DISSERTATION-2018.pdf: 23154163 bytes, checksum: c7cd7ebcadfd297b71165c172c6035ec (MD5) LICENSE.txt: 4208 bytes, checksum: fe3bdd87cee4bfae15a6541b6fe40f33 (MD5) Previous issue date: 2018-11-19","abstract_html":"Made available in DSpace on 2019-02-06T19:36:02Z (GMT). No. of bitstreams: 2 PARE-DISSERTATION-2018.pdf: 23154163 bytes, checksum: c7cd7ebcadfd297b71165c172c6035ec (MD5) LICENSE.txt: 4208 bytes, checksum: fe3bdd87cee4bfae15a6541b6fe40f33 (MD5) Previous issue date: 2018-11-19","abstract_has_math":false,"creators":["Pare, Philip E."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Beck, Carolyn L.","Nedich, Angelia","Başar, Tamer","Srikant, Rayadurgam"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-02-06T19:36:02Z","date_published":"2019-02-06T19:36:02Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Epidemic processes","Virus spread models","Network analysis and control","Networked systems","Stochastic systems","Time-varying systems","Time-varying networks","Network theory (graphs)","Diseases","Biological system modeling","Data models","Mathematical model","John Snow's cholera data set","Validation of networked systems"],"languages":["en"],"rights":["Copyright 2018 Philip E. Pare"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/102436","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Beck, Carolyn L.","Nedich, Angelia","Başar, Tamer","Srikant, Rayadurgam"]},{"key":"dc:creator","label":"Author","values":["Pare, Philip E."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-02-06T19:36:02Z","2018-11-19","2018-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Epidemic processes","Virus spread models","Network analysis and control","Networked systems","Stochastic systems","Time-varying systems","Time-varying networks","Network theory (graphs)","Diseases","Biological system modeling","Data models","Mathematical model","John Snow's cholera data set","Validation of networked systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Philip E. Pare"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/102436"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Made available in DSpace on 2019-02-06T19:36:02Z (GMT). No. of bitstreams: 2 PARE-DISSERTATION-2018.pdf: 23154163 bytes, checksum: c7cd7ebcadfd297b71165c172c6035ec (MD5) LICENSE.txt: 4208 bytes, checksum: fe3bdd87cee4bfae15a6541b6fe40f33 (MD5) Previous issue date: 2018-11-19","The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can provide insights that lead to long-term societal benefits. Basic virus models have been studied for over three centuries; however, as the world continues to become connected and networked in more complex ways, previous models no longer are sufficient. Therefore virus spread over networks is a newer research topic, which provides a compelling modeling technique to capture real world behavior, and interest from the control field has provided an exciting new outlook on the area. Prior research has focused mainly on network models with static graph structures; however, the systems being modeled typically have dynamic graph structures and have not been validated with real spread data over a network. In this dissertation, we consider virus spread models over networks with dynamic graph structures, and we investigate the behavior of these systems. We perform stability analyses of epidemic processes over time-varying networks, providing sufficient conditions for convergence to the disease free equilibrium (the origin, or healthy state), in both the deterministic and stochastic cases. We also explore the scenario of multiple viruses, in the case of competing viruses, including human awareness, and coupled competing viruses. We analyze the healthy state and the endemic states of these models over static and dynamic graph structures. Various control techniques are also proposed to mitigate virus spread in networks. Illustrative figures and simulations are presented throughout. No previous work has explored identification and validation of network dependent virus spread models, which is considered herein using two datasets: 1) John Snow's fundamental 1854 cholera dataset and 2) a 2009-2012 USDA farm subsidy dataset. We conclude by discussing current work and future research directions.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms","The student, Philip Pare, accepted the attached license on 2018-11-16 at 12:33.","The student, Philip Pare, submitted this Dissertation for approval on 2018-11-16 at 13:51.","This Dissertation was approved for publication on 2018-11-19 at 11:45.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13092 on 2019-02-05 at 11:09:17"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Virus spread over networks: Modeling, analysis, and control"]}]}],"canonical_facts":{"dc:contributor":["Beck, Carolyn L.","Nedich, Angelia","Başar, Tamer","Srikant, Rayadurgam"],"dc:creator":["Pare, Philip E."],"dc:date":["2019-02-06T19:36:02Z","2018-11-19","2018-12"],"dc:description":["Made available in DSpace on 2019-02-06T19:36:02Z (GMT). No. of bitstreams: 2 PARE-DISSERTATION-2018.pdf: 23154163 bytes, checksum: c7cd7ebcadfd297b71165c172c6035ec (MD5) LICENSE.txt: 4208 bytes, checksum: fe3bdd87cee4bfae15a6541b6fe40f33 (MD5) Previous issue date: 2018-11-19","The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can provide insights that lead to long-term societal benefits. Basic virus models have been studied for over three centuries; however, as the world continues to become connected and networked in more complex ways, previous models no longer are sufficient. Therefore virus spread over networks is a newer research topic, which provides a compelling modeling technique to capture real world behavior, and interest from the control field has provided an exciting new outlook on the area. Prior research has focused mainly on network models with static graph structures; however, the systems being modeled typically have dynamic graph structures and have not been validated with real spread data over a network. In this dissertation, we consider virus spread models over networks with dynamic graph structures, and we investigate the behavior of these systems. We perform stability analyses of epidemic processes over time-varying networks, providing sufficient conditions for convergence to the disease free equilibrium (the origin, or healthy state), in both the deterministic and stochastic cases. We also explore the scenario of multiple viruses, in the case of competing viruses, including human awareness, and coupled competing viruses. We analyze the healthy state and the endemic states of these models over static and dynamic graph structures. Various control techniques are also proposed to mitigate virus spread in networks. Illustrative figures and simulations are presented throughout. No previous work has explored identification and validation of network dependent virus spread models, which is considered herein using two datasets: 1) John Snow's fundamental 1854 cholera dataset and 2) a 2009-2012 USDA farm subsidy dataset. We conclude by discussing current work and future research directions.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms","The student, Philip Pare, accepted the attached license on 2018-11-16 at 12:33.","The student, Philip Pare, submitted this Dissertation for approval on 2018-11-16 at 13:51.","This Dissertation was approved for publication on 2018-11-19 at 11:45.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13092 on 2019-02-05 at 11:09:17"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/102436"],"dc:language":["en"],"dc:rights":["Copyright 2018 Philip E. Pare"],"dc:subject":["Epidemic processes","Virus spread models","Network analysis and control","Networked systems","Stochastic systems","Time-varying systems","Time-varying networks","Network theory (graphs)","Diseases","Biological system modeling","Data models","Mathematical model","John Snow's cholera data set","Validation of networked systems"],"dc:title":["Virus spread over networks: Modeling, analysis, and control"],"dc:type":["text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:40Z"}