{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108229"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108229","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Mathematical modeling of infectious diseases","abstract":"In this dissertation, we studied mathematical models of infectious diseases that consist of ordinary differential equations (ODEs) and partial differential equations (PDEs). An ODE model is formulated to describe the dynamics of wild mosquitoes when Wolbachia-infected female and male mosquitoes are introduced in the wild as a biological control, where we assume imperfect maternal transmission of Wolbachia to offspring and incomplete cytoplasmic incompatibility. In order to reduce the population of wild mosquitoes with minimal release of Wolbachia-infected mosquitoes in the wild, we develop an optimal control model. The optimal controls are found by using the Pontryagin's Maximum Principle. We also formulated an ODE optimal control model to describe the dynamics of dengue-infected humans when Wolbachia-infected mosquitoes are introduced in the wild along with efforts on educational campaigns to motivate individuals for using personal protection in order to reduce humans-mosquitoes. In this optimal control model, we also determined the most cost-effectiveness control strategy among different control interventions to reduce dengue infections in humans. In the host (Daphnia)- parasite (fungal spores) system, we study the disease dynamics of Daphnia in a water column where both algae and spores sink and diffuse. We formulated the Daphnia-spores-algae model using advection-diffusion partial differential equations (PDEs). We studied the effects of algal carrying capacity, sinking rates of algae and spores, and the water column maximum depth on the disease dynamics of Daphnia.","abstract_html":"In this dissertation, we studied mathematical models of infectious diseases that consist of ordinary differential equations (ODEs) and partial differential equations (PDEs). An ODE model is formulated to describe the dynamics of wild mosquitoes when Wolbachia-infected female and male mosquitoes are introduced in the wild as a biological control, where we assume imperfect maternal transmission of Wolbachia to offspring and incomplete cytoplasmic incompatibility. In order to reduce the population of wild mosquitoes with minimal release of Wolbachia-infected mosquitoes in the wild, we develop an optimal control model. The optimal controls are found by using the Pontryagin's Maximum Principle. We also formulated an ODE optimal control model to describe the dynamics of dengue-infected humans when Wolbachia-infected mosquitoes are introduced in the wild along with efforts on educational campaigns to motivate individuals for using personal protection in order to reduce humans-mosquitoes. In this optimal control model, we also determined the most cost-effectiveness control strategy among different control interventions to reduce dengue infections in humans. In the host (Daphnia)- parasite (fungal spores) system, we study the disease dynamics of Daphnia in a water column where both algae and spores sink and diffuse. We formulated the Daphnia-spores-algae model using advection-diffusion partial differential equations (PDEs). We studied the effects of algal carrying capacity, sinking rates of algae and spores, and the water column maximum depth on the disease dynamics of Daphnia.","abstract_has_math":false,"creators":["Ahmed, Iftikhar"],"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","DeVille, Lee","Zharnitsky, Vadim","Caceres, Carla"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-27T00:46:51Z","date_published":"2020-08-27T00:46:51Z","updated_at":"2026-07-22T22:24:48Z","subjects":["Epidemic Models","Wolbachia","Optimal Control","Daphnia","Dynamical Systems","Partial Differential Equations"],"languages":["en"],"rights":["Copyright 2020 Iftikhar Ahmed"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108229","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rapti, Zoi","DeVille, Lee","Zharnitsky, Vadim","Caceres, Carla"]},{"key":"dc:creator","label":"Author","values":["Ahmed, Iftikhar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-27T00:46:51Z","2022-08-27T00:51:40Z","2020-04-09","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["Epidemic Models","Wolbachia","Optimal Control","Daphnia","Dynamical Systems","Partial Differential Equations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Iftikhar Ahmed"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108229"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation, we studied mathematical models of infectious diseases that consist of ordinary differential equations (ODEs) and partial differential equations (PDEs). An ODE model is formulated to describe the dynamics of wild mosquitoes when Wolbachia-infected female and male mosquitoes are introduced in the wild as a biological control, where we assume imperfect maternal transmission of Wolbachia to offspring and incomplete cytoplasmic incompatibility. In order to reduce the population of wild mosquitoes with minimal release of Wolbachia-infected mosquitoes in the wild, we develop an optimal control model. The optimal controls are found by using the Pontryagin's Maximum Principle. We also formulated an ODE optimal control model to describe the dynamics of dengue-infected humans when Wolbachia-infected mosquitoes are introduced in the wild along with efforts on educational campaigns to motivate individuals for using personal protection in order to reduce humans-mosquitoes. In this optimal control model, we also determined the most cost-effectiveness control strategy among different control interventions to reduce dengue infections in humans. In the host (Daphnia)- parasite (fungal spores) system, we study the disease dynamics of Daphnia in a water column where both algae and spores sink and diffuse. We formulated the Daphnia-spores-algae model using advection-diffusion partial differential equations (PDEs). We studied the effects of algal carrying capacity, sinking rates of algae and spores, and the water column maximum depth on the disease dynamics of Daphnia.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2022-05-01","The student, Iftikhar Ahmed, accepted the attached license on 2020-03-09 at 19:30.","The student, Iftikhar Ahmed, submitted this Dissertation for approval on 2020-03-09 at 19:53.","This Dissertation was approved for publication on 2020-04-09 at 09:53.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14891 on 2020-08-25 at 17:38:59","Made available in DSpace on 2020-08-27T00:46:51Z (GMT). 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An ODE model is formulated to describe the dynamics of wild mosquitoes when Wolbachia-infected female and male mosquitoes are introduced in the wild as a biological control, where we assume imperfect maternal transmission of Wolbachia to offspring and incomplete cytoplasmic incompatibility. In order to reduce the population of wild mosquitoes with minimal release of Wolbachia-infected mosquitoes in the wild, we develop an optimal control model. The optimal controls are found by using the Pontryagin's Maximum Principle. We also formulated an ODE optimal control model to describe the dynamics of dengue-infected humans when Wolbachia-infected mosquitoes are introduced in the wild along with efforts on educational campaigns to motivate individuals for using personal protection in order to reduce humans-mosquitoes. In this optimal control model, we also determined the most cost-effectiveness control strategy among different control interventions to reduce dengue infections in humans. In the host (Daphnia)- parasite (fungal spores) system, we study the disease dynamics of Daphnia in a water column where both algae and spores sink and diffuse. We formulated the Daphnia-spores-algae model using advection-diffusion partial differential equations (PDEs). We studied the effects of algal carrying capacity, sinking rates of algae and spores, and the water column maximum depth on the disease dynamics of Daphnia.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2022-05-01","The student, Iftikhar Ahmed, accepted the attached license on 2020-03-09 at 19:30.","The student, Iftikhar Ahmed, submitted this Dissertation for approval on 2020-03-09 at 19:53.","This Dissertation was approved for publication on 2020-04-09 at 09:53.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14891 on 2020-08-25 at 17:38:59","Made available in DSpace on 2020-08-27T00:46:51Z (GMT). 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