{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/78106"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/78106","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A Stochastic Model for The Transmission Dynamics of Toxoplasma Gondii","abstract":"Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters.","abstract_html":"Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters.","abstract_has_math":false,"creators":["Gao, Guangyue"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Computer Science","degree_department":"Computer Science","school":null,"contributors":[],"advisors":[],"committee_chairs":["Cao, Yang"],"committee_members":["Sun, Shu-Ming","Sandu, Adrian"],"year":2016,"date_issued":"2016-05-05","date_published":"2016-05-05","updated_at":"2026-07-22T22:19:10Z","subjects":["Gillespie Algorithm","Toxoplasma Gondii","Finite Difference Method","Transmission Dynamics","Compartment-Based Model","Stochastic Simulation"],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05112016-210816"],"render_values":[{"text":"etd-05112016-210816","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/78106","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Cao, Yang"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Sun, Shu-Ming","Sandu, Adrian"]},{"key":"dc:contributor.department","label":"Department","values":["Computer Science"]},{"key":"dc:creator","label":"Author","values":["Gao, Guangyue"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-06-13T19:43:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-06-13T19:43:58Z","2016-06-01"]},{"key":"dc:date.issued","label":"Date","values":["2016-05-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Gillespie Algorithm","Toxoplasma Gondii","Finite Difference Method","Transmission Dynamics","Compartment-Based Model","Stochastic Simulation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05112016-210816"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/78106"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["A Stochastic Model for The Transmission Dynamics of Toxoplasma Gondii"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Cao, Yang"],"dc:contributor.committeemember":["Sun, Shu-Ming","Sandu, Adrian"],"dc:contributor.department":["Computer Science"],"dc:creator":["Gao, Guangyue"],"dc:date.accessioned":["2017-06-13T19:43:58Z"],"dc:date.available":["2017-06-13T19:43:58Z","2016-06-01"],"dc:date.issued":["2016-05-05"],"dc:description.abstract":["Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. 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