Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if Rv < 1, and disease invades if Rv > 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when R̅v < 1, and I(t) is persistent with sustained oscillations when R̅v > 1. Numerical simulations indicate that the orbit representing I(t) decays when R̅v < 1 < Rv. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease in the maximum of prevalence of infectives upon the introduction of routine vaccination and a sustained decrease as pulse vaccination is introduced in the population.
Mortality data of pneumonia and influenza is collected and analyzed. A decomposition of the data is analyzed, trend and seasonality effects ascertained, and a forecasting strategy proposed.
","abstract_html":"<p>Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if <em><b>R</b><sub>v</sub></em> < 1, and disease invades if <em><b>R</b><sub>v</sub></em> > 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when <em><b>R̅</b><sub>v</sub></em> < 1, and <em>I</em>(<em>t</em>) is persistent with sustained oscillations when <em><b>R̅</b><sub>v</sub></em> > 1. Numerical simulations indicate that the orbit representing <em>I</em>(<em>t</em>) decays when <em><b>R̅</b><sub>v</sub></em> < 1 < <em><b>R</b><sub>v</sub></em>. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease in the maximum of prevalence of infectives upon the introduction of routine vaccination and a sustained decrease as pulse vaccination is introduced in the population.</p><p>Mortality data of pneumonia and influenza is collected and analyzed. A decomposition of the data is analyzed, trend and seasonality effects ascertained, and a forecasting strategy proposed.</p>","abstract_has_math":false,"creators":["Numfor, Eric Shu"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-12-18T08:00:00Z","date_published":"2010-12-18T08:00:00Z","updated_at":"2026-07-24T02:20:55Z","subjects":["Epidemics","Basic reproduction number","Seasonality","Vaccination","Epidemiology","Medicine and Health Sciences","Public Health"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1745","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Numfor, Eric Shu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2010-12-18T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"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":["Epidemics","Basic reproduction number","Seasonality","Vaccination","Epidemiology","Medicine and Health Sciences","Public Health"]}]},{"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/3100/viewcontent/NumforE082310f.pdf","https://dc.etsu.edu/etd/1745"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if Rv < 1, and disease invades if Rv > 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when R̅v < 1, and I(t) is persistent with sustained oscillations when R̅v > 1. Numerical simulations indicate that the orbit representing I(t) decays when R̅v < 1 < Rv. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease in the maximum of prevalence of infectives upon the introduction of routine vaccination and a sustained decrease as pulse vaccination is introduced in the population.
Mortality data of pneumonia and influenza is collected and analyzed. A decomposition of the data is analyzed, trend and seasonality effects ascertained, and a forecasting strategy proposed.
"]},{"key":"dc:title","label":"Title","values":["Mathematical Modeling, Simulation, and Time Series Analysis of Seasonal Epidemics."]}]}],"canonical_facts":{"dc:creator":["Numfor, Eric Shu"],"dc:date.issued":["2010-12-18T08:00:00Z"],"dc:description.abstract":["Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if Rv < 1, and disease invades if Rv > 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when R̅v < 1, and I(t) is persistent with sustained oscillations when R̅v > 1. Numerical simulations indicate that the orbit representing I(t) decays when R̅v < 1 < Rv. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease in the maximum of prevalence of infectives upon the introduction of routine vaccination and a sustained decrease as pulse vaccination is introduced in the population.
Mortality data of pneumonia and influenza is collected and analyzed. A decomposition of the data is analyzed, trend and seasonality effects ascertained, and a forecasting strategy proposed.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3100/viewcontent/NumforE082310f.pdf","https://dc.etsu.edu/etd/1745"],"dc:rights":["Copyright by the authors."],"dc:subject":["Epidemics","Basic reproduction number","Seasonality","Vaccination","Epidemiology","Medicine and Health Sciences","Public Health"],"dc:title":["Mathematical Modeling, Simulation, and Time Series Analysis of Seasonal Epidemics."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:20:55Z"}