East Tennessee State University
Mathematical Modeling, Simulation, and Time Series Analysis of Seasonal Epidemics.
Abstract
dc:description.abstract<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>
Degree
thesis:*- Name thesis:degree_name
- MS (Master of Science)
- Level thesis:degree_level
- Thesis - unrestricted
- Discipline thesis:degree_discipline
- Mathematical Sciences
- Year dc:date.issued
- 2010
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Numfor, Eric Shu
Subjects
dc:subject × 7Rights
dc:rights- Statement dc:rights
-
- Copyright by the authors.
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://dc.etsu.edu/etd/1745
- OAI identifier oai:identifier
- oai:dc.etsu.edu:etd-3100