Agent based modeling of Eciton burchelli swarm patterns

Jose Almora, University of North Carolina, Chapel Hill
Albert Izarraraz, University of California, Irvine
Qiao Liang, University of New Mexico, Albuquerque
Crystal Nesmith, St. Mary's College of Maryland

MTBI-01-2M
Poster sessions award recipient at the National 2005 AMS convention in Atlanta, GA
Abstract: Eciton burchelli is a unique species of army ants that demonstrate non-traditional swarm behavior. These ants have extremely poor eyesight and as a result, they rely heavily on the distribution and tracking of pheromone. In order to identify mechanisms that generate a scaled down nest and food conditions of E.burchelli, we create a simulated ant world using agent based modeling. The hope is that simple rules will generate the desired emergent behavior. We propose various ant behavioral rules and observe the generated (emerging) swarm patterns. The focus of this study is on the exploration of the role of pheromone directional intensity on swarming dynamics. We test various factors on the agents and their impact on pheromone trails; key elements in the survival of the E.burchelli colony. In addition to the simulations, existing models of swarm behavior (reaction-diffusion-advection PDE's) are analyzed and their dynamics are compared with the results from the simulations.

USA the Fast Food Nation: Obesity as an Epidemic

Arlene Morales Evangelista, Arizona State University
Angela R. Ortiz, Arizona State University
Karen R.Ros-Soto, Cornell University
Alicia Urdapilleta, Arizona State University

MTBI-01-3M

Abstract: For the last 20 years, the prevalence of overweight and obesity has increased dramatically in the United States. Now, the problem of obesity is of epidemic proportions. Statistics show that approximately 1 out of 3 people in the United States are obese. Research indicates that fast-food is partly to blame for the growth observed increases in obesity and overweight. Over the last three decades, fast-food has infiltrated the American way of life. Fast food restaurant has become a prominent feature of the diet of many Americans. The aim of this project is to study the role of peer-pressure in fast-food consumption as well as its potential effects on individuals weight at the population level. We explore the impact of changes on the dynamics of fast-food eating behaviors. Statistical data analysis is employed to study the relation of demographic factors and weight.

Does gravitational gossip weigh heavy on your local area network (LAN)?

Reynaldo Castro-Estrada, Arizona State University
Anthony Billups, Northeastern University
Wilbert Fernandez, Arizona State University

MTBI-01-4M

Abstract: The World Wide Web has proven useful in disseminating information. However, it is extremely difficult to track its spread in such complex network. One simplification is to model it as a small Local Area Network. Previous work has shown that a gossip-based multicast can be an effective tool for modeling the flow of information on a local area network. We examine the effect of different networks within this mathematical framework. We propose a general mathematical model that incorporates the susceptibility and infectivity of a given machine in a local area network. We also use the concept of proportionate mixing to model the spread of information among heterogeneous patches, where each patch consists of users an non-users of an information router.

The Role of Vaccination in the Control of SARS

Julijana Gjorgjieva, Harvey Mudd College
Kelly Smith, Clarion University
Jessica Snyder, Georgia Institute of Technology
Gerardo Chowell, Cornell University
Fabio Sánchez, Cornell University

MTBI-01-5M
Poster sessions award recipient at the National 2004 SACNAS convention in New Orleans, LA

Abstract: In this paper we explore pre-outbreak and during-outbreak vaccination as control strategies for SARS epidemics. We construct a mathematical model that includes susceptible, latent (traced and untraced), infectious, quarantined/isolated, recovered, and dead classes. Using data from the 2002-2003 SARS outbreak in Hong Kong (China), we assume different scenarios where the percentage of traced infectious contacts and untraced individuals that self-quarantine varies. We predict the minimal necessary proportion of the population that needs to be successfully vaccinated prior to an outbreak to control an epidemic. We calculate the basic reproductive number, R₀, and carry out an uncertainty and sensitivity analysis. The final epidemic size under different vaccination scenarios is estimated. Vaccination is shown to be a good control strategy to reduce the total epidemic size with an increased impact when combined with effective isolation of the quarantined/isolated individuals.

Modeling of Tumor Growth and its Control via Paclitaxel Using a Delay Differential Equation

Yi Lin, Emory University
Kevin Flores, University of California, Santa Barbara
Lauren Hannah, Princeton Univeristy

MTBI-01-6M

Abstract: Paclitaxel is shown to be antiangiogenic at low doses, but the extent of these effects is not known. A mathematical model that describes tumor growth and response to treatment with a continuous, low dose treatment of the anti-mitotic drug Paclitaxel is considered. The model considers 3 populations: system cells, proliferating tumor cells, and tumor cells in a resting phase. A time delay accounts for the time it takes for tumor cells to complete one cycle in the proliferation phase. The system is first analyzed without drug administration, and then analyzed numerically under different levels of drug administration. We provide a rigorous analysis of a three dimensional differential equation system with a single delay. Finally, sensitivity analysis is performed on certain parameters to determine what the likely consequences of antiangiogenic effects.

HIV and Its Impact on the Infant Immune System

Antonio Buenrostro, San Diego State University
Katie Diaz, Columbia University
C. P. Gonzales, Arizona State University
Magdaliz Gorritz, University of Texas San Antonio

MTBI-01-7M

Abstract: Many models have been developed which illustrate the interaction between the HIV virus and the immune system of adult individuals. However, limited work has been attempted in efforts to explain the interaction between HIV and an infant's immune system. In this study, we introduce a model that considers the dynamics between CD4⁺ T cells, CD8⁺ T cells, and the HIV virus. Analysis of the model gives rise to a threshold parameter, Ncrit, which is the critical number of  new viruses produced by an actively infected CD4⁺ T cells. Numerical simulations are carried out, and sensitivity analysis is performed on Ncrit to illustrate the differences between the progression of HIV in infants as compared to that in adults.

The Impact of Mosquito-Bird Interaction on the Spread of West Nile Virus to Human Populations

Diego Chowell-Puente, Universidad de Colima
Pablito Delgado, University of New Mexico Albuquerque
David Perez, Loyola Marymount University
Cynthia Hixahuary Sanchez Tapia, Universidad de Colima
Fabio Sánchez, Cornell University
David Murillo, Arizona State University

MTBI-01-8M

Abstract: West Nile Virus (WNV) is a rapidly spreading and potentially fatal disease that presents a public health challenge. In this study, we develop a mixed Susceptible-Infected and Susceptible-Infected-Recovered model for WNV dynamics that includes mosquito, bird and human populations. We calculate the basic reproductive number (R₀) and establish the existence of possible multiple endemic equilibria. The sensitivity of R₀ to parameters is studied. The possibility of multiple equilibria when R₀ < 1 (backward bifurcations) implies that standard control measures are likely to be inadequate to control an epidemic.