{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/90745"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/90745","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stochastic and deterministic multipatch epidemic models","abstract":"This dissertation covers the modeling of epidemics in populations that contain multiple groups that also includes interaction between subgroups. The main techniques employed are thresholds for both the deterministic and the stochastic system through an approximating multi-type branching process. We formulate a continuous time Markov Chain that corresponds to each deterministic system studied. The main idea will be to study the spectral radius of the next generation matrix with regards to crossing of a critical threshold (corresponding to stability) with regards to the parameter $\\gamma$, which measures the amount of interaction between each of the groups. We include numerical approximations of the ordinary differential equation (ODE). We also derive how the continuous time is an actual approximation through the theory of Darling and Norris. We further give examples of comparing all three: spectral data, the actual ODE numerical results, and the stochastic approximation. We further study how modifying the parameters modifies the properties of the model. Multiple examples for each model are given in both the paper and the end material. We also discuss how the graph structure modifies the ability of an epidemic to spread.","abstract_html":"This dissertation covers the modeling of epidemics in populations that contain multiple groups that also includes interaction between subgroups. The main techniques employed are thresholds for both the deterministic and the stochastic system through an approximating multi-type branching process. We formulate a continuous time Markov Chain that corresponds to each deterministic system studied. The main idea will be to study the spectral radius of the next generation matrix with regards to crossing of a critical threshold (corresponding to stability) with regards to the parameter <span class=\"etd-inline-math\">&gamma;</span>, which measures the amount of interaction between each of the groups. We include numerical approximations of the ordinary differential equation (ODE). We also derive how the continuous time is an actual approximation through the theory of Darling and Norris. We further give examples of comparing all three: spectral data, the actual ODE numerical results, and the stochastic approximation. We further study how modifying the parameters modifies the properties of the model. Multiple examples for each model are given in both the paper and the end material. We also discuss how the graph structure modifies the ability of an epidemic to spread.","abstract_has_math":true,"creators":["Hasler, Jordan J"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["DeVille, Lee","Rapti, Zoi","Zharnitsky, Vadim","Kirkpatrick, Kay"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T20:27:13Z","date_published":"2016-07-07T20:27:13Z","updated_at":"2026-07-22T22:26:34Z","subjects":["epidemics","dynamical systems","stochastic processes","SIR"],"languages":["en"],"rights":["Copyright 2016 Jordan Hasler"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/90745","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["DeVille, Lee","Rapti, Zoi","Zharnitsky, Vadim","Kirkpatrick, Kay"]},{"key":"dc:creator","label":"Author","values":["Hasler, Jordan J"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-07-07T20:27:13Z","2018-07-08T09:15:30Z","2016-04-15","2016-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["epidemics","dynamical systems","stochastic processes","SIR"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Jordan Hasler"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/90745"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation covers the modeling of epidemics in populations that contain multiple groups that also includes interaction between subgroups. The main techniques employed are thresholds for both the deterministic and the stochastic system through an approximating multi-type branching process. We formulate a continuous time Markov Chain that corresponds to each deterministic system studied. The main idea will be to study the spectral radius of the next generation matrix with regards to crossing of a critical threshold (corresponding to stability) with regards to the parameter $\\gamma$, which measures the amount of interaction between each of the groups. We include numerical approximations of the ordinary differential equation (ODE). We also derive how the continuous time is an actual approximation through the theory of Darling and Norris. We further give examples of comparing all three: spectral data, the actual ODE numerical results, and the stochastic approximation. We further study how modifying the parameters modifies the properties of the model. Multiple examples for each model are given in both the paper and the end material. We also discuss how the graph structure modifies the ability of an epidemic to spread.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01","The student, Jordan Hasler, accepted the attached license on 2016-04-11 at 18:27.","The student, Jordan Hasler, submitted this Dissertation for approval on 2016-04-11 at 18:33.","This Dissertation was approved for publication on 2016-04-15 at 09:56.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9189 on 2016-07-07 at 13:49:03","Made available in DSpace on 2016-07-07T20:27:13Z (GMT). No. of bitstreams: 3 HASLER-DISSERTATION-2016.pdf: 1760419 bytes, checksum: 0630a67d22ccbc92e5a0280f111ac867 (MD5) LICENSE.txt: 4210 bytes, checksum: 8a9aa2820892333b62a2b2d9f5fa75f8 (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 98888290a315ebd10266b26dcad3020b (MD5) Previous issue date: 2016-04-15","Embargo set by: Seth Robbins for item 93097 Lift date: 2018-07-07T20:28:14Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 93097 Lift date: 2018-07-07T20:35:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 93097 on 2018-07-08T09:15:30Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Stochastic and deterministic multipatch epidemic models"]}]}],"canonical_facts":{"dc:contributor":["DeVille, Lee","Rapti, Zoi","Zharnitsky, Vadim","Kirkpatrick, Kay"],"dc:creator":["Hasler, Jordan J"],"dc:date":["2016-07-07T20:27:13Z","2018-07-08T09:15:30Z","2016-04-15","2016-05"],"dc:description":["This dissertation covers the modeling of epidemics in populations that contain multiple groups that also includes interaction between subgroups. The main techniques employed are thresholds for both the deterministic and the stochastic system through an approximating multi-type branching process. We formulate a continuous time Markov Chain that corresponds to each deterministic system studied. The main idea will be to study the spectral radius of the next generation matrix with regards to crossing of a critical threshold (corresponding to stability) with regards to the parameter $\\gamma$, which measures the amount of interaction between each of the groups. We include numerical approximations of the ordinary differential equation (ODE). We also derive how the continuous time is an actual approximation through the theory of Darling and Norris. We further give examples of comparing all three: spectral data, the actual ODE numerical results, and the stochastic approximation. We further study how modifying the parameters modifies the properties of the model. Multiple examples for each model are given in both the paper and the end material. We also discuss how the graph structure modifies the ability of an epidemic to spread.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01","The student, Jordan Hasler, accepted the attached license on 2016-04-11 at 18:27.","The student, Jordan Hasler, submitted this Dissertation for approval on 2016-04-11 at 18:33.","This Dissertation was approved for publication on 2016-04-15 at 09:56.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9189 on 2016-07-07 at 13:49:03","Made available in DSpace on 2016-07-07T20:27:13Z (GMT). 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