Session Chair: Dr. Jean-Marie Pages, The Citadel
2:15-2:30 Jhacova A. Williams, Xavier University of Louisiana
Computer Simulations for the Discrete Model of West Nile-Like Epidemics
The spread of the West Nile Encephalitis is modeled with the system of non-autonomous nonlinear difference equations. Model was introduced by Thomas and Urena and later modified and generalized by Darensburg and Kocic. The model consists of a system twelve difference equations representing the effects of the West Nile-Like Virus on populations of birds, humans, and mosquitoes. The effects of spraying to control the population of mosquitoes are also incorporated in the model. In this paper computer simulations are used to study the dynamics of the model when different spraying strategies are applied.
2:35-2:50 Daniela Valdez-Jasso, North Carolina State University
Developing a viscoelastic model for arteries
When deriving one-dimensional fluid dynamic models of blood flow in arteries it is necessary to include a constitutive equation. Typically such models relate cross-sectional area of the artery to blood pressure. Most previous constitutive equations are based on elastic or empirical models. However, it has long been known that arteries display viscoelatic properties. In this work we present a viscoelastic model relating blood pressure and cross-sectional area and validate this model against data obtained from pigs. Using measured pressure data as an input, we used nonlinear optimization to compute model parameters that minimized the difference between computed and measured values of the cross-sectional area. With this optimization we were able to obtain high coherence between our model and data and, furthermore, we showed that the viscoelastic model was able to predict the data significantly better than a traditional elastic model.
2:55-3:10 Michael D. Phillips, East Tennessee State University,
with Istvan Karsai and Jeff Knisley
Division of Labor in Social Wasp Colonies: An Agent-Based Approach
Social insect colonies develop into parallel processing systems in which the colony conducts most of its operations concurrently instead of sequentially. Recently, theories of self-organization have explained this behavior by using local information to provide a better understanding of the complexity and dynamics present in these systems. Social wasp colonies provide some of the clearest views of self-organization in biological systems. In particular, wasp nest construction provides a great opportunity to study division of labor.
An ODE mathematical model of the division of labor in wasp colonies was developed by Karsai and Balazsi (2002). We build on this earlier work with a bottom-up modeling approach. To study the decentralized decision making in these colonies we propose an agent-based model that prohibits individual access to global information and ensures that all interactions take place on a local level.
Using only a few simple mechanisms, we have created a model that accurately predicts the division of labor in social wasp colonies. With only a few simple behavioral rules and no central control present, the model is able to predict a great amount of complexity and capture the dynamics of the natural system.