{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105612"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105612","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Mathematical models of daphnia epidemics","abstract":"Disease ecology studies the interactions among hosts, pathogens, and the environment and how these shape the spread of disease. These interactions can be quite complex and lead to fascinating dynamics. Our system of study, Daphnia has a lot of interesting and complex features that can be analyzed with precision both biologically and mathematically. By using mathematical models we can study the underlying biological mechanisms that drive and/or inhibit the spread of disease. This dissertation explores, through a range of models, the many aspects that play a role in Daphnia epidemics. We begin with simple models and build models with higher complexity by adding more realistic biological assumptions. From ordinary and partial differential equation models to stochastic models, through the chapters of this thesis, we zoom-in to the different aspects of Daphnia epidemics and and zoom-out to the bigger story that connects them. We give precise conditions under which short-term evolution of hosts can lead to the early termination of an epidemic. Moreover, overturning an assumption about hosts’ ability to recover, we showcase the role of recovery from an infection in reducing disease prevalence and the number of secondary infections. Through this thesis we have gained more insight into the biology of our system, and more importantly we open the door to new and exciting questions. As new biological insights are discovered, we can use mathematical models to continue to unravel the many aspects of Daphnia epidemics.","abstract_html":"Disease ecology studies the interactions among hosts, pathogens, and the environment and how these shape the spread of disease. These interactions can be quite complex and lead to fascinating dynamics. Our system of study, Daphnia has a lot of interesting and complex features that can be analyzed with precision both biologically and mathematically. By using mathematical models we can study the underlying biological mechanisms that drive and/or inhibit the spread of disease. This dissertation explores, through a range of models, the many aspects that play a role in Daphnia epidemics. We begin with simple models and build models with higher complexity by adding more realistic biological assumptions. From ordinary and partial differential equation models to stochastic models, through the chapters of this thesis, we zoom-in to the different aspects of Daphnia epidemics and and zoom-out to the bigger story that connects them. We give precise conditions under which short-term evolution of hosts can lead to the early termination of an epidemic. Moreover, overturning an assumption about hosts’ ability to recover, we showcase the role of recovery from an infection in reducing disease prevalence and the number of secondary infections. Through this thesis we have gained more insight into the biology of our system, and more importantly we open the door to new and exciting questions. As new biological insights are discovered, we can use mathematical models to continue to unravel the many aspects of Daphnia epidemics.","abstract_has_math":false,"creators":["Rivera Quinones, Vanessa"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rapti, Zoi","Laugesen, Richard","DeVille, Lee","Caceres, Carla"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:33:42Z","date_published":"2019-11-26T20:33:42Z","updated_at":"2026-07-22T22:24:44Z","subjects":["disease ecology","rapid evolution","Daphnia","epidemic models","recovery","host-parasite","resource competition","Quantitative Genetics","Adaptive Dynamics","mathematical models","Partial differential equations","Stochastic models","Gillespie Algorithm"],"languages":["en"],"rights":["Copyright 2019 Vanessa Rivera Quinones"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105612","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rapti, Zoi","Laugesen, Richard","DeVille, Lee","Caceres, Carla"]},{"key":"dc:creator","label":"Author","values":["Rivera Quinones, Vanessa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:33:42Z","2019-07-01","2019-08"]},{"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":["disease ecology","rapid evolution","Daphnia","epidemic models","recovery","host-parasite","resource competition","Quantitative Genetics","Adaptive Dynamics","mathematical models","Partial differential equations","Stochastic models","Gillespie Algorithm"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Vanessa Rivera Quinones"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105612"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Disease ecology studies the interactions among hosts, pathogens, and the environment and how these shape the spread of disease. These interactions can be quite complex and lead to fascinating dynamics. Our system of study, Daphnia has a lot of interesting and complex features that can be analyzed with precision both biologically and mathematically. By using mathematical models we can study the underlying biological mechanisms that drive and/or inhibit the spread of disease. This dissertation explores, through a range of models, the many aspects that play a role in Daphnia epidemics. We begin with simple models and build models with higher complexity by adding more realistic biological assumptions. From ordinary and partial differential equation models to stochastic models, through the chapters of this thesis, we zoom-in to the different aspects of Daphnia epidemics and and zoom-out to the bigger story that connects them. We give precise conditions under which short-term evolution of hosts can lead to the early termination of an epidemic. Moreover, overturning an assumption about hosts’ ability to recover, we showcase the role of recovery from an infection in reducing disease prevalence and the number of secondary infections. Through this thesis we have gained more insight into the biology of our system, and more importantly we open the door to new and exciting questions. As new biological insights are discovered, we can use mathematical models to continue to unravel the many aspects of Daphnia epidemics.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms","The student, Vanessa Rivera Quinones, accepted the attached license on 2019-06-20 at 16:22.","The student, Vanessa Rivera Quinones, submitted this Dissertation for approval on 2019-06-20 at 16:23.","This Dissertation was approved for publication on 2019-07-01 at 10:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14057 on 2019-11-26 at 12:50:00","Made available in DSpace on 2019-11-26T20:33:42Z (GMT). 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Our system of study, Daphnia has a lot of interesting and complex features that can be analyzed with precision both biologically and mathematically. By using mathematical models we can study the underlying biological mechanisms that drive and/or inhibit the spread of disease. This dissertation explores, through a range of models, the many aspects that play a role in Daphnia epidemics. We begin with simple models and build models with higher complexity by adding more realistic biological assumptions. From ordinary and partial differential equation models to stochastic models, through the chapters of this thesis, we zoom-in to the different aspects of Daphnia epidemics and and zoom-out to the bigger story that connects them. We give precise conditions under which short-term evolution of hosts can lead to the early termination of an epidemic. Moreover, overturning an assumption about hosts’ ability to recover, we showcase the role of recovery from an infection in reducing disease prevalence and the number of secondary infections. Through this thesis we have gained more insight into the biology of our system, and more importantly we open the door to new and exciting questions. As new biological insights are discovered, we can use mathematical models to continue to unravel the many aspects of Daphnia epidemics.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms","The student, Vanessa Rivera Quinones, accepted the attached license on 2019-06-20 at 16:22.","The student, Vanessa Rivera Quinones, submitted this Dissertation for approval on 2019-06-20 at 16:23.","This Dissertation was approved for publication on 2019-07-01 at 10:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14057 on 2019-11-26 at 12:50:00","Made available in DSpace on 2019-11-26T20:33:42Z (GMT). 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