Date of Award

2016

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Luis F. Gordillo

Abstract

The growth of a two-sex population is undoubtedly dependent upon the dynamics of its mating encounter rates. Encounter rates are influenced by several factors that affect the modeling of a population. In this work we first look at the law of mass action as applied to mating encounter rates. We review the underlying assumptions of mass action and present a derivation using dimensional reduction and simulated data. This approach led to a revised proportionality constant that seems to produce results in better accord to experimental data than does the original constant. We also explore numerically how random fluctuations on the revised constant affect the conditioned time to extinction of a two-sex population subject to reproductive Allee effect. Next we present an application to pest management. We consider the effectiveness of chemosterilant induced infertility in a rat population and present qualitative predictions for population behavior when subject to this fertility control. We look at the dynamics of both a spatially isolated rat population and a population with multiple rat communities where individual movement between patches occur.

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