Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

12-2010

Committee Chair or Co-Chairs

Ariel Cintron-Arias

Committee Members

Robert B. Gardner, Jeff R. Knisley

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.

Document Type

Thesis - unrestricted

Copyright

Copyright by the authors.

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