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Summer 2000
A Mathematical Model for Lung Cancer: The Effects of Second-Hand Smoke and Education
Carlos Acevedo-Estefanía, University of Puerto Rico-Cayey
Christina González, Texas A&M University
Karen Ríos-Soto, University of Puerto Rico-Mayagez
Eric Summerville, St. Mary's University
Project supervisors: Baojun Song, Cornell University
Carlos Castillo-Chávez, Cornell University
BU-1525-M
Poster sessions award recipient at the National 2000 SACNAS convention in Atlanta, GA
Abstract:
In the United States, lung cancer is the leading cause of cancer deaths. As of today, cigarette smoking causes 85% of lung cancer deaths. In this study, a non-linear system of differential equations is used to model the dynamics of a population, which includes smokers. The parameters of the model are obtained from data published by cancer institutes, health and government organizations. The average number of individuals who become smokers and the reduction of this average by an education program are determined. The long-term impact of educating a susceptible class before they enter the population model and the effect it has on the epidemic (getting lung cancer) is also studied. Simulations using realistic parameters are carried out to illustrate our theoretical results.
A Socially Transmitted Disease: Teacher Qualifications and High School Drop-Out Rates
Corvina Boyd, Arizona State University
Alison Castro, University of California, Riverside
Nicolas M. Crisosto, University of California, Berkeley
Arlene Evangelista, Arizona State University
Project supervisors:
Christogher Kribs-Zaleta, University of Texas, Arlington
Carlos Castillo-Chávez, Cornell University
BU-1526-M
Poster sessions award recipient at the National 2001 Joint Mathematics Meeting (AMS, MAA, AWM & NAM) in New Orleans, LA
Oral presentation award recipient at the California Alliance for Minority Participation (CAMP)
Conference at UC-Davis, April 2001. (Speaker: Alison Castro)
Abstract:
The main goal of this study is to quantify the impact of teacher interactions on student achievement to facilitate recommending policy strategies that minimize high school dropout rates. This study derives a system of differential equations that examine the effects that teachers have on minority high school students' learning experience in California and Arizona. The first mathematical model focuses on the impact that teacher dynamics have on a school's faculty composition. Teacher's dynamics are coupled with a second system that models student responses to teacher preparation and experience in order to investigate the effects of these interactions on high school dropout and completion rates.
Do we really have to take all our medicine? Predicting the Consequences of Large-Scale Antibiotic Misuse
Caroline Cutting, Massachusetts Institute of Technology
Claudia Morales, University of Alabama-Huntsville
Fabio Sánchez, Universidad Metropolitana-Cupey>
Deena Schmidt, The University of Akron
Project supervisors:
Baojun Song, Cornell University
Carlos Hernández-Suarez, Universidad de Colima - México
BU-1527-M
Abstract: Failure to properly complete antibiotic treatments can result in the eventual development of bacterial strains resistant to antibiotic therapy. If present trends in antibiotic misuse continue, infections that are easily treated today may not be so in the future. We consider a stochastic model and use Markov chain analysis to examine the conditions of misuse under which resistant strains will thrive. Virulence differences in the competing strains are taken into consideration, as is the possibility of superinfection. The probability of extinction is calculated for each strain. We predict the long-term effects of antibiotic misuse and consider the specific case of Streptococcus pneumoniae, the bacteria that cause pneumonia.
Evolution of Fluconazole Resistance in Candida albicans
Omayra Ortega, Pomona College
Nnaemeka Anyadike, Virginia Commonwealth University
Aaron Greenblatt, Duke University
Project supervisors:
Martin Engman, Universidad Metropolitana-Cupey
Stephen Wirkus, Cornell University
BU-1528-M
Abstract: The opportunistic fungus Candida albicans is found naturally in the human body. The immune system normally keeps the fungus safely in check; however given an immunodeficient or immuno-impaired host, the fungus population can grow to harmful levels. Hence, Candida albicans often afflicts HIV and cancer patients. Antifungal agents called azoles are used to treat Candida albicans. Resistant strains develop through natural mutations and flourish when the antifungal agents are not implemented correctly. These resistant strains of Candida albicans can coexist with non-resistant strains. In this study we assume that if an antifungal agent is used after the resistant strains have developed, the antifungal agent will only be effective in killing the susceptible strain, while the resistant strain can survive, but with reduced virulence. Resistance to antifungal treatment in a given population of Candida albicans is modeled via a system of nonlinear differential equations. This model is used to study the development of resistant strains of Candida albicans due to improper use of azoles, specifically fluconazole.
The Effects of a Potential National Campaign and a VEI Type Vaccine on an HIV-1 Infected Homosexually Active Population
José Alvarado, University of Puerto Rico-Cayey
Oscar Estrada, Universidad Autónoma de Ciudad Juárez
Emily Kajita, Harvey Mudd College
Nadia Monrose, University of the Virgin Islands
Project supervisor:
Carlos Hernández-Suarez, Universidad de Colima - México
BU-1529-M
Poster sessions award recipient at the National 2000 SACNAS convention in Atlanta, GA
Poster sessions award recipient at the National 2001 Joint Mathematics Meeting (AMS, MAA, AWM & NAM) in New Orleans, LA
Abstract: We build a stochastic model to analyze the dynamics of HIV in a homosexually active population. In our model, we introduce the effects of a hypothetical campaign that promotes HIV testing as well as the effect of a VEI (Vaccine Efficacy for Infectiousness) type vaccine. We analyze how the efficacy of the vaccine and campaign affect disease dynamics, particularly the probability of eventual extinction of the disease. The general conclusion is that increasing the efficacy of the vaccine results in a higher probability of extinction of the epidemic as expected. However, increasing the efficacy of the campaign above some optimum counter-intuitively decreases the probability of extinction. We find the minimum efficacy of the vaccine and the optimum efficacy of the campaign to drive the epidemic to extinction.
Dynamics of Two-Strain Influenza with Isolation and Cross-Immunity
Miriam Nuño. Claremont Graduate University
Project supervisor:
Carlos Castillo-Chávez, Cornell University
BU-1530-M
Abstract: The evolution of influenza type A virus is tightly linked to a non-fixed evolutionary landscape driven by tight co-evolutionary interactions between hosts and influenza strains. Cross-immunity, host isolation, and age-structure are three important factors responsible for the coexistence and dynamics of multiple strains of influenza. Here, it is shown that cross-immunity and host isolation is enough to support the possibility of multi-strain epidemics. In fact, sustained oscillations with reasonable periods are possible. We establish the possibility via Hopf-bifurcation theory, and illustrate our results with simulations. The length of the period agrees with reported data.
Dispersal between Two Patches in a Discrete Time SEIS Model
Brisa N. Sanchez, University of Texas-El Paso
Paula A. González, Universidad del Valle, Cali, Colombia
Roberto A. Sáenz, Universidad Autónoma de Cd. Juarez
Project supervisors:
Abdul-Aziz Yakubu, Howard University
Carlos Castillo-Chávez, Cornell University
BU-1531-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.
Deterministic and Stochastic Reaction-Diffusion Models in a Ring
Gerardo Chowell, Universidad de Colima
Sara Del Valle, New Jersey Institute of Technology
Dulcie Kermah, Howard University
Leisis Martino, Barry University
Project supervisor:
Juan Pablo Aparicio, Cornell University
BU-1532-M
Abstract: For an epidemic to occur, infectious individuals have to generate at least one secondary infection before they die or recover. A simple model is introduced where epidemic states are possible when the number of secondary infections caused by an individual is less than 1. Models with varying levels of complexity in the population dynamics are introduced and the question of whether or not they force or drive disease epidemic patterns is analyzed in a single and multiple patch system connected by dispersal. Interaction of this sort between patches can disrupt the initial one patch disease dynamics; for example dispersal can cause a disease-free equilibrium where otherwise there would be none.
Discrete-Time S-E-I-S Models with Exogerous Re-infection and Dispersal between Two Patches
Rogelio Arreola, University of California at Irvine
Aldo Crossa, Wittenberg University, Springfield
Maria Cristina Velasco, Universidad del Valle, Cali, Colombia
Project supervisor:
Abdul-Aziz Yakubu, Howard University
BU-1533-M
Abstract: Typically, for an epidemic to occur, infectious individuals have to generate at least one secondary infection before they die or recover (R0 >1). A simple model is introduced where epidemics are possible when R0 <1. Models with varying levels of complexity in the population dynamics are introduced and the question of whether or not they force or drive disease epidemic patterns is analyzed in a single and multiple patch system connected by dispersal. Interaction of this sort between patches can disrupt the initial one patch disease dynamics; for example, dispersal can cause a disease-free equilibrium where otherwise there would be none.