Date of Award
Master of Science (MS)
Mathematics and Statistics
Luis F. Gordillo
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.
Snyder, Katherine R., "Modeling of Mating Encounters: The Classical Mass Action Paradigm and an Application to Pest Control" (2016). All Graduate Plan B and other Reports. 807.