Seminar Series in Applied Mathematics
Dr. Louis Rossi, University of Delaware
Modeling and Analyzing Large Swarms
Animal groups often exhibit social behaviors that lead to aggregations. Examples include schools of fish, flocks of birds and cohorts of pedestrians. These aggregations serve a variety of functions including navigational guidance, protection, foraging and so forth. At the same time, scientists and engineers look to swarming in nature for inspiration on the design and control of large numbers of mobile, autonomous systems that interact through wireless communication. We summarize recent efforts to develop and analyze useful descriptions of large swarms using continuum models. We focus our efforts on behavior driven by three-zone swarming. In three-zone swarming behavior, the action of an individual is driven by the position and orientation of neighboring individuals in each of three concentric zones. An individual will try to move away from others in the innermost zone of repulsion. An individual will try to align itself with others in the central zone of orientation. Finally, an individual will try to move toward individuals in the outermost zone of attraction. Individual behavior is the weighted contribution from the three influences. The fundamental purpose of this research is to understand how interactions between individuals are mapped to the motion and properties of the entire swarm. We are particularly interested in the stability of coherent structures within a given system, information transfer within swarms, the role of memory in swarming behavior and leadership within swarms. We will provide an overview of recent results on these facets of swarm dynamics.
Dr. Hem Raj Joshi, Xavier University
The Influence of Education Reducing the HIV Epidemics
Throughout the world, the HIV epidemic continues to pose major problems for health care. While researchers are still trying to find a cure, other efforts are being made to decrease the spread of HIV by increasing awareness through education. One of these campaigns presented by Uganda's government was the ABC campaign, which promotes Abstinence, Be Faithful, and Condoms to decrease the spread of HIV. The HIV/AIDS infection rates have decreased significantly due to organizations promoting this campaign and other educational information. A SIRE model will be used to evaluate the effectiveness of these organizations on the HIV epidemic of Uganda. Changed behavior as a result of the campaign will create a new SIRE model based on this campaign and divide those susceptible into four different subgroups. These four susceptible classes will have different infection rates due to their differing beliefs on sexual conducts. The model is a system of ordinary differential equations in which data from Uganda about the epidemic and educational influences will be used to help estimate the parameters of infection rates and run model simulations.
Dr. Donald A French, University of Cincinnati
Modeling the Spread of Alcohol Abuse - Differential Equations on Networks
In the last decade there have been significant advances, mainly through the availability of vast amounts of data and fast computers, in our understanding of the structure of social networks. In this talk we discuss our work on modeling the spread of alcohol abuse by incrementally more extensive mathematical models. We start with a single logistic-type differential equation, progress to a system of equations and end with a network model