This thesis discusses limit cycles and behavior of rumor models. The first part presents the deterministic Daley-Kendall model (DK) with arrivals and departures and comparison of the Susceptibles, Infectives and Removed (SIR) model and the DK model. The second result is a part of the qualitative analysis and the general behavior of extension of the Daley-Kendall model. Here we discuss how the halting rate of spreaders causes the model to change from a stable equilibrium or a stable limit cycle. In the third part we carry out model validation and use both synthetic data and real data sets and fit them to the numerical solutions of the extended Daley-Kendall model. Finally, we find the parameter estimates and standard errors. In this way we shall be able to decide whether the numerical solutions quantifying the relationships between the variables obtained from the qualitative analysis can be accepted as the best description of the data. We discuss sensitivity analysis results and traditional sensitivity functions.
","abstract_html":"<p>This thesis discusses limit cycles and behavior of rumor models. The first part presents the deterministic Daley-Kendall model (DK) with arrivals and departures and comparison of the Susceptibles, Infectives and Removed (SIR) model and the DK model. The second result is a part of the qualitative analysis and the general behavior of extension of the Daley-Kendall model. Here we discuss how the halting rate of spreaders causes the model to change from a stable equilibrium or a stable limit cycle. In the third part we carry out model validation and use both synthetic data and real data sets and fit them to the numerical solutions of the extended Daley-Kendall model. Finally, we find the parameter estimates and standard errors. In this way we shall be able to decide whether the numerical solutions quantifying the relationships between the variables obtained from the qualitative analysis can be accepted as the best description of the data. We discuss sensitivity analysis results and traditional sensitivity functions.</p>","abstract_has_math":false,"creators":["Odero, Geophrey Otieno, Mr."],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - restricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-12-01T08:00:00Z","date_published":"2013-12-01T08:00:00Z","updated_at":"2026-07-24T02:20:06Z","subjects":["Basic reproduction number","Halting rate","Sensitivity analysis.","Applied Mathematics","Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1236","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Odero, Geophrey Otieno, Mr."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-08-12T07:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-12-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - restricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Basic reproduction number","Halting rate","Sensitivity analysis.","Applied Mathematics","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/2419/viewcontent/Limit_Cycles_and_Dynamics_of_Rumor_Models.pdf","https://dc.etsu.edu/etd/1236"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis discusses limit cycles and behavior of rumor models. The first part presents the deterministic Daley-Kendall model (DK) with arrivals and departures and comparison of the Susceptibles, Infectives and Removed (SIR) model and the DK model. The second result is a part of the qualitative analysis and the general behavior of extension of the Daley-Kendall model. Here we discuss how the halting rate of spreaders causes the model to change from a stable equilibrium or a stable limit cycle. In the third part we carry out model validation and use both synthetic data and real data sets and fit them to the numerical solutions of the extended Daley-Kendall model. Finally, we find the parameter estimates and standard errors. In this way we shall be able to decide whether the numerical solutions quantifying the relationships between the variables obtained from the qualitative analysis can be accepted as the best description of the data. We discuss sensitivity analysis results and traditional sensitivity functions.
"]},{"key":"dc:title","label":"Title","values":["Limit Cycles and Dynamics of Rumor Models"]}]}],"canonical_facts":{"dc:creator":["Odero, Geophrey Otieno, Mr."],"dc:date.available":["2013-08-12T07:00:00Z"],"dc:date.issued":["2013-12-01T08:00:00Z"],"dc:description.abstract":["This thesis discusses limit cycles and behavior of rumor models. The first part presents the deterministic Daley-Kendall model (DK) with arrivals and departures and comparison of the Susceptibles, Infectives and Removed (SIR) model and the DK model. The second result is a part of the qualitative analysis and the general behavior of extension of the Daley-Kendall model. Here we discuss how the halting rate of spreaders causes the model to change from a stable equilibrium or a stable limit cycle. In the third part we carry out model validation and use both synthetic data and real data sets and fit them to the numerical solutions of the extended Daley-Kendall model. Finally, we find the parameter estimates and standard errors. In this way we shall be able to decide whether the numerical solutions quantifying the relationships between the variables obtained from the qualitative analysis can be accepted as the best description of the data. We discuss sensitivity analysis results and traditional sensitivity functions.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2419/viewcontent/Limit_Cycles_and_Dynamics_of_Rumor_Models.pdf","https://dc.etsu.edu/etd/1236"],"dc:rights":["Copyright by the authors."],"dc:subject":["Basic reproduction number","Halting rate","Sensitivity analysis.","Applied Mathematics","Mathematics"],"dc:title":["Limit Cycles and Dynamics of Rumor Models"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - restricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:20:06Z"}