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Summer 2003
Change in Host Behavior and its Impact on the Co-evolution of Dengue
C. P. Gonzales ,
Colorado State University
K. Herman, North Carolina Agricultural and Technical Stat University
D. Murillo, Arizona State University
Fabio Sánchez, Cornell University
BU-1639-M
Poster sessions award recipient at the National 2004 AMS convention in Phoenix, AZ
Abstract: The joint evolutionary dynamics of dengue strains
are poorly understood despite its high prevalence around the world. Two
dengue strains are put in competition in a population where behavioral
changes can affect the probability of infection. The destabilizing dynamic
effect of even "minor" behavioral changes is discussed and their role in
dengue control is explained.
Mathematical Model for Photoreceptor Interaction
Miguel Angel Colón Vélez, University of Puerto Rico
Daniel Jesus Hernández, Boston University
Ubaldo Rodriguez Bernier, University of Puerto Rico
Jon Van Laarhoven, Lawrence University
Erika Camacho, Los
Alamos National Laboratory
BU-1640-M
Poster sessions award recipient at the National 2003 SACNAS convention in Albuquerque, NM
Abstract: The retina is arguably the single most important component in the vision process. Via its photoreceptors it is responsible for converting electromagnetic radiation into a chemical signal understandable by the brain. The interactions between rod and cones in the retina have been the focus of innumerable experimental and theoretical biological studies in previous decades, yet the understanding of these interactions is still in its infancy. We develop mathematical models which address the possibilities of direct photoreceptor interactions through horizontal cells as well as indirect interactions via an intermediary trophic factor. We address the role these means of communication play in the presence of the degenerative disease, Retinitis pigmentosa. The diseased system exhibits a fold-Hopf bifurcation. Biological interpretation of all systems is given with the long-term objective of using our results to aid in prevention of vision loss in retinally degenerative diseases.
Modeling a Novel Method to Control Human Malaria: Insecticide Treated Cattle
Ana Franco, Los Alamos
National Laboratory
BU-1641-M
Abstract: Malaria, a re-emergent vector-borne disease, has always had a deep impact on the health and economy of a large percentage of the world population. In areas where malaria vectors also feed on animals, the presence of livestock impacts the risk of disease transmission to humans. Treatment of livestock, with insecticides that are fatal to the vector, has been proposed as a novel approach in malaria control. Promising results have been observed from trials in Pakistan. However, several factors underlying the effectiveness of insecticide treated livestock remain poorly understood. This study looks at the relevance of some of these factors including coverage treatment levels and vector preference. We expand on the Ross-Macdonald framework through the incorporation of vector feeding behaviors. The main focus of this research is to understand the circumstances under which a policy that involves the systematic use of insecticides on livestock will decrease the prevalence of human malaria.
A Deterministic Approach to the Spread of Rumors
K. Thompson, Howard University
R. Castro Estrada, Universidad Metropolitana
D. Daugherty, California State Polytechnic University
A. Cintrón-Arias,
Cornell Universtiy
BU-1642-M
Abstract: Ideas, products and messages spread in ways that resemble the transmission dynamics of viruses. We begin with the same framework as Daley-Kendall, which classifies individuals as susceptibles, "spreaders", and "stiflers", and models rumor spreading as an epidemic. We look at the implications of heterogeneity in the susceptible and spreader classes on the spread of a rumor, an aspect not considered in the Daley-Kendall model. Finally, the dynamics of rumor spreading in chat rooms that are accessible to a large number of groups are explored under the assumption of simple, local (neighborhood) dynamics. The characterization of dynamics is carried out through a combination of analytical and numerical results. Efforts to determine the most effective ways to stop or accelerate the spread of rumors are also discussed.
The Role of Network Topology on the Initial Growth Rate of Influenza Epidemic
Shilpa Khatri, New York University
Rosalyn Rael, University of Arizona
J. Hyman, Los Alamos National Laboratory
BU-1643-M
Abstract: We use networks, powerful abstract representations of systems of interacting elements, to represent multiple interacting populations and explore the effects of the topologies on the initial growth rate of influenza epidemics. Graph theory applied to epidemiological models may yield insight into the nature of disease dynamics and provide important complementary perspective on understanding these models. We analyze the basic SIR model on three general networks: ring, square lattice, small world networks. We explore the evolution of the dominant eigenvalues as the network size increases for two different cases, when the total population remains constant and when the total population increases as the network size increases. The analysis is carried out via numerical simulations as well as through the mathematical analysis of simple cases.
Scaling Laws and Dynamics of Sexual Activity with Interracial and Multi-Ethnic Mixing
J. Bracamonte, South Mountain Community College
M. Gorritz, University of Texas at San Antonio
G. Martinez, California Polytechnic University
C. Nesmith, St. Mary's College of Maryland
G. Chowell, Cornell
University
BU-1644-M
Abstract: A stochastic model that simulates the processes of pair formation and dissolution among interracial and multi-ethnic mixing groups is presented. Extensive simulations are carried out with the probabilities of mixing and pair-dissolution taken from published data and specific parametric families of distributions. Scaling laws associated with the distribution of partnerships, the average number of partners and its variability are identified. Connections to recent work on scale-free and small world networks are discussed.
Katie Diazrlene, Mills College - Oakland
Cassie Fett, Bemidji State University - Bemidji
Griselle Torres-Garcia, University of Puerto Rico - Mayaguez
Nicolas M. Crisosto, UC
Berkeley-Berkeley
BU-1645-M
Abstract: We develop a model that incorporates the impact of sudden-teacher ratio on the performance dynamics of both teachers and students. The model assumes that the members of both populations may be found in three dynamics states: positive, discouraged and reluctant. The role of complex nonlinear interactions between students and teachers, as well as the role of recruitment and intervention, are studied via analytic and numerical studies. Using center manifold theory we find conditions for the existence of a backward bifurcation that support endemic stationary states below the critical threshold value, R0 < 1, when normally only a positive environment would be supported. Our simulations show that in order to maintain a positive environment for students and teachers, R0 must be reduced significantly. Since R0 is a function of student-teacher ratio this can be achieved by decreasing class size.