Degree Name

MS (Master of Science)


Mathematical Sciences

Date of Award


Committee Chair or Co-Chairs

Ariel Cintron-Arias

Committee Members

Robert B. Gardner, Jeff R. Knisley


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 v < 1, and I(t) is persistent with sustained oscillations when v > 1. Numerical simulations indicate that the orbit representing I(t) decays when v < 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 - Open Access


Copyright by the authors.

Included in

Epidemiology Commons