Date of Award

12-2014

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

David E. Hiebeler

Second Committee Member

Ramesh Gupta

Third Committee Member

Andrew Knightly

Abstract

The SIS (Susceptible-Infected-Susceptible) epidemiological model is used to describe the spread of diseases which do not confer immunity to infected individuals. A model in which an SIS epidemic spreads through a population which is subdivided into communities is explored. Individuals in the communities interact with others locally (within the community) and globally (with individuals from other communities). The dynamics of the proportion of infected individuals per community are described with a set of differential equations, supported by data from computer simulations, with the goal of measuring how the adjustment of various parameters affects two types of statistical variance. Increasing the proportion of local interactions increases the variance of the proportion of infected individuals per household, but it has little effect on the variance of the infection level between different populations.

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