Term of Award

Fall 2018

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Divine Wanduku

Committee Member 1

Broderick Oluyede

Committee Member 2

stephen carden

Abstract

Influenza ranks among the top ten most important diseases in the USA. In fact, the CDC estimates that between 12 - 56 thousand deaths occur annually since 2010. In this study, we present a stochastic chain-binomial model for the dynamics of in-fluenza in a closed human population. We consider treatment for the disease in the form of vaccination, and incorporate the periods of effectiveness of the vaccine and infectiousness. Our model is an SVIR model, where all individuals who recover from the disease acquire natural immunity. The transition probabilities are presented for two scenarios depending on whether the events of infectiousness and vaccination are dependent. The parameters of the model are estimated using the maximum likeli- hood method and the EM algorithm. Some epidemiological assessment parameters, such as the basic reproduction number and probability of no spread, are computed. Numerical simulation examples are presented for the model.

OCLC Number

1085541980

Research Data and Supplementary Material

No

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