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Summer 1998
A Mathematical Model for Assessing Genetic Damage on HIV Populations after Anti-Retroviral Therapy
Ileana Borjas, Universidad Nacional Autónoma de México
Meera Lea Pradhan, University of Texas
Magnon Ivan Reyes, Florida International University
Kenneth Jeremy Spencer, Texas A&M University
BU-1506-M
Poster sessions award recipient at the National 1998 SACNAS convention in Washington, DC
Abstract:
AZT, an anti-retroviral drug, kills a large proportion of HIV in a patient's body. Those killed tend to be "highly fit"; that is, they are well adapted to the environment of the body and those that survive are poorly fit. As time passes by, the small proportion of strains that survive the medication have a chance of mutating into strains of higher fitness. From this phenomenon, we find a unique angle to analyze these dynamics. Instead of the perspective of the population of HIV strains. Combining genetic algorithms and difference equations, we attempt to assess the genetic damage of one drug on the future generations of survivors. We use the model of difference equations to compare the viral load of the current generation to its predecessors. The genetic algorithms allow us to analyze strains of DNA in terms of binary sequences instead of nucleotides. In the simulations we can analyze the long term behavior of the population against a drug. The goal is to describe a therapy that prevents the population of HIV from exploding.
The Effects of Condom Distribution with Education on Chlamydia Rates in High Schools
Cristina Garcia, Pomona College
Sharon Lima, University of Iowa
Roberto Munoz-Alicea, University of Puerto Rico-Humacao
Catalina Saenz, Wellesley College
BU-1507-M
Abstract: In 1996 the Center for Disease Control reported that adolescents account for the largest proportion of Chlamydia cases. One method discussed by experts to control Chlamydia rates is education and condom distribution in high schools. This report analyzes a stochastic process and deterministic models to determine the effectiveness of condom distribution with education, in controlling the transmission of Chlamydia amongst high school students.
A Stochastic Study of Incarceration Times for Narcotic Distributors in a City under "The Three Strikes Law"
Jaime H. Barrera, Cornell University
Carlos Melgar, University of California- Riverside
Joaquin Rivera-Cruz, University of Iowa
BM-1508-M
Abstract: Narcotics ruins peoples' lives in the United States everyday. The United States government not only imposes stiff sentences on drug dealers but also spends billions of dollars a year developing programs to try to reduce the high intensity of drug distribution in cities across the United States. Unfortunately there is still a high number of narcotics being distributed within the United States. We use a stochastic model to study the trends of drug dealer populations set into motion as a result of fixing a set of incarceration times for drug dealers. We then project these trends and calculate costs associated with jailing drug dealers and the associated active drug dealer distributions. Specific questions that we are address include: Do a fixed set of incarceration times set trends in drug dealer populations? For a fixed set of incarceration times, how much does it cost to jail drug dealers 5 years? For 10 years? What do these costs buy? Are there less drug dealers as a result of these policies?
Discussion of Difference Equation Model of Ventricular Parasystole as an Interaction between Cardiac Pacemakers Based on the Phase Response Curve
Nandi Leslie, Howard University
Alicia Simms, Universidad Nacional Autónoma de México
Miriam Nuño, Claremont Graduate University
BU-1509-M
Abstract: A ventricular parasystole is a cardiac rhythm resulting from an irregular discharge of an ectopic pacemaker to the sinoatrial node (sinus pacemaker). The intrinsic cycle length of the ectopic pacemaker is influenced by the impulses of the sinus pacemaker. This influence is described by a phase response curve (PRC). The stimulus phase of a ventricular parasystole is modeled by a discontinuous difference equation developed from the PRC by Ikeda et al. This study analyzes the periodic solutions of Ikeda et al. (1983) difference equation with different phase response curves.
Dynamical Results of Discrete Pioneer and Climax Species Models
Agustín Izquierdo-Sabido, Universidad Nacional Autónoma de México
Carmen Martínez-Trigo, Universidad Nacional Autónoma de México
Mark Suluc Muktoyuk, University of Arizona
Abdul-Aziz Yakubu, Howard University
BU-1510-M
Abstract: Two types of species, pioneer and climax species, are modeled. When the functions describing the dynamics of these species satisfy certain assumptions, we show limitations of the dynamics within these species, both as independent and as competing species.
The Effect of Purse Seine Vessel Harvesting in the Eastern Tropical Pacific Yellowfin Tuna Stock
Saul Franco, University of California-Irvine
Ignacio Méndez-Gómez-Humarán, El Colegio de la Frontera Norte
Ricardo Ortiz-Rosado, Universidad de Puerto Rico-Cayey
Daniel Sánchez-Araiza, California State University-Dominguez Hills
BU-1511-M
Abstract: In the eastern tropical Pacific, the purse-seine vessels captures yellowfin tuna as target species under three different fishing modes. We are interested in modeling the influence of these three different fishing modes in the tuna stock. We propose a system of differential equations to model the stock dynamics with proportional harvesting. We analyze a rescaled version of the model where a basic reproductive number was obtained and interpreted in terms of the original parameters. The basic reproductive number was analyzed to study the effect of critical harvesting levels for each fishing mode. Finally we developed some numerical solutions using approximated parameters to study the effect of harvesting on the tuna stock dynamics.
Estimation of the Population Vaccination Effectiveness Using Urn Models
Carlos Barrera-Rodríguez, Universidad Autónoma Metropolitana, México
Ariel Cintrón-Arias, University of Puerto Rico-Cayey
Angelina Espinoza-Limón, Universidad Autónoma Metropolitana, México
Dulce Vargas-Bracamontes, Universidad de Colima, México
Carlos Hernández-Suarez, Universidad de Colima, México
BU-1512-M
Abstract:
Dispersal and dormancy are two of the fundamental evolutionary mechanisms used by nature to support and generate ecological diversity. In this investigation, we focus on the role of disease-enhanced or disease-suppressed dispersal on the dynamics of populations in a multi-patch system. Single patch systems, which are capable of supporting simple and complex dynamics, are studied both analytically and numerically. The impact of disease and dispersal is also studied numerically. Our results are compared to those in the literature that focused on dispersal in disease free multi-patch systems.
pulation vaccination effectiveness (PVE) is defined as the fraction of disease cases prevented by a vaccination campaign. We use occupancy urn models to estimate the PVE, and compare results for leaky, all-or-nothing and VEI (vaccine efficacy for infectiousness) vaccines using data of a measles outbreak and San Francisco current AIDS epidemic. This latter motivated by the current development of HIV vaccines of the VEI type. When applying our method to predict PVE for the San Francisco AIDS epidemic, our model predicts that PVE will he relatively low, even if the fraction of vaccinated and the efficacy of the vaccine are high.
The Recovery and Ecological Succession of the Tropical Montserrat Flora from Periodic Volcanic Eruptions
Daniella Costo, California State University Sacramento
Lisa Denogean, California Polytechnic State University Pomona
Akuba Dolphyne, Wellesley College
Carrie Mello, University of California Riverside
Carlos Castillo-Garsow, Cornell University
BU-1513-M
Abstract: The island of Montserrat, located in the British West Indies, experiences periodic volcanic eruptions that destroy major regions of the indigenous plant life and leaves lasting damage from volcanic pollution. This project intends to model the process that occurs as this damaged tropical ecosystem recovers from volcanic eruptions. We will use a stochastic model to study the ecological succession after volcanic disturbances. We expect to see a redistribution of the diversity of plant life according to the different levels of devastation. The simulations of recovery should show that after a period of time, a large region of the recovered plant life will reach an equilibrium without risk of extinction.