{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-1735"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-1735","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC MODELS IN MATHEMATICAL EPIDEMIOLOGY","abstract":"We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions.","abstract_html":"We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions.","abstract_has_math":false,"creators":["Tosun, Kursad"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Schurz, Henri"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-01T07:00:00Z","date_published":"2013-08-01T07:00:00Z","updated_at":"2026-07-24T04:34:11Z","subjects":["Balanced Implicit Method","Mathematical Epidemiology","Stochastic Asymptotic Stability","Stochastic SIR Model","Stochastic SIS Model"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/732","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schurz, Henri"]},{"key":"dc:creator","label":"Author","values":["Tosun, Kursad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-12-10T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Balanced Implicit Method","Mathematical Epidemiology","Stochastic Asymptotic Stability","Stochastic SIR Model","Stochastic SIS Model"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/732"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions."]},{"key":"dc:title","label":"Title","values":["QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC MODELS IN MATHEMATICAL EPIDEMIOLOGY"]}]}],"canonical_facts":{"dc:contributor":["Schurz, Henri"],"dc:creator":["Tosun, Kursad"],"dc:date.available":["2015-12-10T08:00:00Z"],"dc:description.abstract":["We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/732"],"dc:subject":["Balanced Implicit Method","Mathematical Epidemiology","Stochastic Asymptotic Stability","Stochastic SIR Model","Stochastic SIS Model"],"dc:title":["QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC MODELS IN MATHEMATICAL EPIDEMIOLOGY"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:34:11Z"}