Physical Sciences and Mathematics Commons^™

Optimal Control Of Epidemic Models Involving Rabies And West Nile Viruses, Timothy Joseph Clayton

Doctoral Dissertations

This research considers the application of Optimal Control theory to minimize the spread of viral infections in disease models. The population models under consideration are systems of ordinary differential equations and represent epidemics arising due to either rabies or West Nile virus. Optimal control strategies are analyzed using Pontryagin’s Maximum Principle and illustrated based upon computer simulations.

The first model describes a population of raccoons and its interaction with the rabies virus, thus dividing the animals into four classes: susceptible, exposed, immune, and recovered (SEIR). The model includes a birth pulse during the spring of the year and …

Parallel Simulation Of Individual-Based, Physiologically-Structured Population And Predator-Prey Ecology Models, Jeffrey A. Nichols

Doctoral Dissertations

Utilizing as testbeds physiologically-structured, individual-based models for fish and Daphnia populations, techniques for the parallelization of the simulation are developed and analyzed. The techniques developed are generally applicable to individual-based models. For rapidly reproducing populations like Daphnia which are load balanced, then global birth combining is required. Super-scalar speedup was observed in simulations on multi-core desktop computers.

The two populations are combined via a size-structured predation module into a predator-prey system with sharing of resource weighted by relative mass. The individual-based structure requires multiple stages to complete predation.

Two different styles of parallelization are presented. The first distributes both populations. …

Zero-Divisor Graphs, Commutative Rings Of Quotients, And Boolean Algebras, John D. Lagrange

Doctoral Dissertations

The zero-divisor graph of a commutative ring is the graph whose vertices are the nonzero zero-divisors of the ring such that distinct vertices are adjacent if and only if their product is zero. We use this construction to study the interplay between ring-theoretic and graph-theoretic properties. Of particular interest are Boolean rings and commutative rings of quotients.