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Summer 2002
The Effect of the HIV/AIDS Epidemic on the Population of Truck Drivers in South Africa and its Economic Impact
Melanie Lee, University of California-Los Angeles
Christine Román, St. Mary's University of San Antonio
Shari Wiley, University of Arkansas-Pine Bluff
Carlos Hernández Suárez, Universidad de Colima-México
Christopher Kribs Zaleta, University of Texas-Arlington
Ricardo Oliva, Cornell University
BU-1612-M
Abstract: As of the end of 2001, an estimated 28,500,000 people in Sub-Saharan Africa (SSA) had been infected with the HIV virus, making up 70% of the world's population of HIV-infected people. Such an aggressive epidemic has not only impacted the SSA demography, but also the African economy and culture. The epidemic has begun to seriously damage the transport sector, where long distance truck drivers (TDs) are at an increased risk of infection due to their frequent contacts with commercial sex workers (CSWs). The spread of AIDS in the transport industry is especially significant to the SSA economy as truck drivers are largely responsible for transporting crops and supplies needed for daily subsistence. In this project we present four mathematical models that describe the interaction between the TDs and CSWs from various perspectives. From the analysis and simulation of these models we qualify the decrease in the TD population due to the HIV/AIDS epidemic and discuss its impact on the transportation industry and the SSA economy in general.
Models of Negatively Damped Harmonic Oscillators: the Case of Bipolar Disorder
Darryl Daugherty, California Polytechnic University, Pomona
John Urea, California State University, Fullerton
Tairi Roque, California State University, Fullerton
Dr. Stephen Wirkus, California Polytechnic University
BU-1613-M
Abstract: Bipolar II disorder is characterized by alternating hypomanic and major depressive episodes. A negatively damped harmonic oscillator is used to model the periodic mood variations of a single bipolar II individual. Treatment is modeled via a function that is capable of stabilizing, within some boundaries, the mood variation of the patient. In this paper we study the dynamics of two individuals with bipolar II disorder who interact with each other. The interaction of two subjects living together who experience bipolar II disorder is modeled via two weakly coupled weakly damped harmonic oscillators.
A Stochastic Approach for Modeling Treatment and Diagnosis of Attention Deficit Disorder
Carlos Acevedo-Estefanía, University of Texas-Austin
Carlos Torre, Cornell University
Ariel Cintrón-Arias, Cornell University
Carlos Hernandez-Suárez, Universidad de Colima-México
Sophonie Nashinyabakobeje, Cornell University
BU-1614-M
Abstract: Attention Deficit Disorder (ADD) is the most common type of mental disorder affecting children. It is estimated that, on the average, 6% of the total United States population is affected by this disorder. The exact causes have not been identified yet, although studies show that there is a genetic component. Our aim is to build an individual based mathematical model that includes the efficiency of the current treatment for ADD. We use a Markov chain approach to model the transitions through different states in a population of children. The asymptotic distribution of the population is computed as a function of the limiting probability of the transition probability matrix. The ratio of children without the disorder to children with disorder as a function of the probability of treatment efficiency is simulated and implications of variations on this ratio as a function of key parameters is described. The importance of early and efficient treatment as well as diagnosis are highlighted through sensitivity analyses performed on the model.
Intraspecific Competition in the Population of Danaus plexippus (L.)
Roberto Sáenz, University of Texas at El Paso
Julie Stein, New College of Florida
Aziz Yakubu, Howard University
Laura Jones, Cornell University
Nancy Tisch, Cornell University
BU-1615-M
Abstract: We propose and analyze a model to describe the population cycles of the monarch butterfly. The annual migration of the monarch involves four generations with mixed reproductive strategies in each generation. Members of generations 1 through 3 (occasionally 4) migrate from the over-wintering site in central Mexico to breeding grounds that extend as far north as the northern United States and southern Canada. A portion of the third generation and all members of the fourth generation begin their return to the over-wintering grounds in August through October where they enter reproductive diapause for several months. We developed a discrete time model in which two different fecundity functions are used in several ways to model the reproductive strategies of each generation. The fecundity functions are selected from broad classes of functions used in ecology. The selection of the type of fecundity function used with each generation is based on biological observations. The objectives of our research are multiple and include the study of the generationally dependent intraspecific competition and its effect on the pool size of migrants as well as the persistance of the overall butterfly populations. The stage structure used in modeling the monarch butterfly dynamics and their generationally-dependent reproductive strategies naturally support fluctuating patterns and multiple attractors. The implications of these fluctuations and attractors on the long-term survival of the monarch butterfly population is explored analytically and through simulations. The impact of our work on conservation biology is discussed.
A Mathematical Model of Depression in Young Women as a Function of the Pressure to be "Beautiful"
Jennifer L. Dillon, Mills College
Natalia Baeza, University of Alabama, Huntsville
Mary Cristina Ruales, University of Puerto Rico at Mayagüez
Baojun Song, Cornell University
BU-1616-M
Abstract: We develop a mathematical model based on the hypothesis that one of the most significant causes of major depressive disorder in young women is the pressure they are under from the media and their peers to attain a stereotypical model of "beauty". Empirical evidence supports the view that the U.S. media's archetype of beautiful women has adverse effects on their mood and self-esteem. The media's impact is moderated by individual differences in the level of internalization of the thin-figure archetype. Diminishing the role of the media is impractical. Hence our model focuses on identifying the means by which women become vulnerable to its effects. It is assumed that women enter the system in one of two classes -- a high vulnerability and a low vulnerability group. Once in the system, peer pressure will drive women's movement between these two groups. The impact of the flow between the two vulnerability groups, treatment and relapse are explored using a nonlinear system of four differential equations.
Chronic Wasting Disease: The Effects of Environmental Prion Density and Interactions between Populations on Disease Dynamics
Paul Hurtado, University of Southern Colorado
Marcin Mejran, Stanford University
Thela Morales, Mesa State College
David Schwager, Cornell University
Michael Lanham, Oxford University - UK
BU-1617-M
Abstract: Chronic wasting disease (CWD) is a degenerative and fatal prion disease affecting cervid (deer and elk) populations in North America. While the disease exists in captive herds throughout the western United States and southern Canada, the only free-ranging populations afflicted are in northern Colorado, southeastern Wyoming, and the western panhandle of Nebraska. CWD, similar to other prion diseases such as scrapie in sheep, bovine spongiform encephalopathy in cattle, and Creutzfeldt-Jacob disease in humans, attacks the central nervous system via an accumulation of abnormal prion proteins. For this investigation we use both analytical and computational approaches to model the dynamics of the disease in mule deer populations. We focus on modifying the structure of an existing model, integrating sources of infection previously excluded from other CWD models. We proceed to model the effects of two interacting populations and the subsequent impact on disease dynamics. We hope that our analysis and simulations will help in the development of spatial models to be used in CWD management, a central goal of wildlife management agencies.
The Effects of Mass Transportation during a Deliberate Release of Smallpox Emilia Huerta-Sánchez, Cornell University
Guarionex Jordan-Salivia, University of Iowa
Karen R. Rios-Soto, Cornell University
Juan Zhang, Xi'an Jiaotung University
BU-1618-M
Abstract:
Since the attack on the world trade center, in New York City on September 11th, the possibility of bio-terrorist attacks on major cities has received continuous attention. The deliberate release of smallpox, a deadly virus, still available in selected U.S. and Russian laboratories, is a source of great concern. Ring vaccination is the current official response policy in the event of smallpox deliberate release. Edward H. Kaplan, David L. Craft and, Lawrence M. Wein argue that mass vaccination is a more viable solution that would optimize resource usage and minimize the mortality rate. In this paper, we model the dynamics of a deliberate release of smallpox in an idealized model of public transportation system of a major city. The city is divided into n neighborhoods and stratified by the proportion of individuals who use public transportation. Two levels of mixing are introduced via within neighborhood and between neighborhood activity level. Transmission between neighborhoods is driven by interactions in the mass transportation system under the assumption of proportionate mixing. We complement our theoretical work with an agent based model for two populations of individuals with different proportions of subway and non-subway users. We explore the impact of Kaplan, Craft and, Wein vaccination policy on the spread of epidemics on both models and our initial results seem to support their recommendations.
The Demographic Effects of Increasing Anthropogenic Noise on Mysticeti Whales
Iván E. Cao-Berg, Universidad Metropolitana
Nathaniel David Mercaldo, University of Idaho
Shirley Eva Sánchez, Rensselaer Polytechnic Institute
Nancy Tisch, Cornell University
Abdul-Aziz Yakubu, Howard University
Abstract:
Over the past five decades anthropogenic (man-made) noise has increased in the world's oceans due to an eruption in shipping, oil drilling, research activities, and military explorations. All these factors have contributed to a dramatic elevation of low frequency noise in the oceanic environment. Research on marine mammals has shown that noise below 500Hz can cause physical trauma to their auditory system. Due to their reliance on their auditory system for survival any drastic increase in noise may compromise their survival. The species in the suborder Mysticeti communicate in frequency ranges from 50-600Hz and thus most affected by increased noise, specifically the six species that are on the endangered species list. We propose that increased oceanic noise will have a deleterious effect on mating and thus reproduction by masking a percentage of mating calls. In order to investigate how noise affects their population dynamics, we modeled the population of Mysticeti whales through a nonlinear system of three discrete time equations (reproductive females, reproductive males, and parental females). Analytical and numerical techniques are used to examine the long-term behavior of our system.
A Critical Response Stochastic Model for Foot-and-Mouth Disease Epidemics
Johnsie Ortiz, Universidad de Puerto Rico-Cayey
Manuel A. Rivera, Universidad Metropolitana (PR)
Daniel Rubin, Stanford University
Israel Ruiz, Universidad de Puerto Rico-Cayey
Carlos M. Hernández, Universidad de Colima - Mexico
Carlos Castillo-Chávez, Cornell University
Abstract:
In this work, we analyze the spread of Foot-and-Mouth Disease (FMD) in Uruguay using three different tools: a deterministic model, a continuous-time Markov chain stochastic model and an explicit stochastic simulation model. The deterministic model, a system of nonlinear ordinary differential equations, uses the cow as the basic epidemiological unit. We compute the basic reproductive number, R0, for a system that differentiates between beef and dairy populations of cows. R0 is used to study FMD persistence and control. In the stochastic model, the basic epidemiological unit is the farm. The impact of a policy that isolates farms is explained. The conditions for quarantine rate that eradicate the disease are computed. The computer simulation model takes into account the coordinates of farms, traffic between them, and type of farm (dairy or beef). It simulates the epidemic in Uruguay, and attempts to predict the regions of Uruguay where quarantine could be a viable national control measure in response to an index case.
A Two-Gender Human Papillomavirus Model with an Investigation of the Effects of Male Screening
Jennifer Froelich, University of North Dakota
Zanetta Gant, Alabama A&M University
Aveek Majumdar, Cornell University
Reyes M. Ortiz-Albino, University of Iowa
Michael Lanham, Oxford University
Abstract:
The Human Papillomavirus (HPV) is the most common sexually transmitted infection in the United States. Though few of its more than one hundred strains cause the recognized symptoms of genital warts, HPV's numerous high-risk strains are highly correlated with cervical cancer cases. HPV's symptoms are gender specific since men and women exhibit different degrees of infectiousness and varied symptoms of infection from high-risk strains of HPV. Men rarely exhibit symptoms and are therefore silent carriers of these carcinogenic agents. In this investigation, we focus on the dynamics of a high-risk strain, HPV16, in a heterosexual population. A two-sex model is used to highlight the impact of asymptomatic infectious males on the dynamics of cervical cancer cases. Hence, we concentrate on the effects that increased HPV detection in males might have on the spread of this virus in a heterosexual population, and the incidence of cervical cancer cases associated with HPV16.
The Effects of Environmental Pressure and Genetic Predisposition to Temperamental Behavior
Bárbara Rivera, University of Puerto Rico-Río Piedras
Griselle Torres-García, University of Puerto Rico-Mayagüez
Alicia Urdapilleta, Mills College
Carlos M. Hernández-Suárez, Universidad de Colima - Mexico
Abstract:
Violent crime can be considered a social epidemic in our society. Although the idea that violence has biological components is not a new one, recent research in genetics has helped to clarify it. However, environmental pressures are essential for an individual to develop violent behavior. In this study, we use a Mendelian model of two alleles at a single locus, where A and a represents low and high predisposition to temperamental behavior. We use a stochastic compartmental model to investigate the dynamics of the population by controlling the environmental and genetic factors and incorporating the effect of interaction with violent people. This study of the dynamics of the population allows us to predict changes in parameters, which in turn may decrease temperamental behavior individuals in the next generations.
Preventing Crack Babies: Different Approaches of Prevention
Angela Ortiz, Universidad Metropolitana (PR)
David Murillo, Cornell University
Fabio Sanchez, Cornell University
Christopher Kribs-Zaleta, Univeristy of Texas-Arlington
Abstract:
Crack-cocaine use among pregnant women is of major social and public health concern for many reasons including the birth of "crack babies" and its relations to HIV infection. Many programs exist that focus on the rehabilitation of women and mothers who use cocaine. We use deterministic and stochastic approaches to model the effectiveness of these programs among particular groups. The focus will be on populations of women (often commercial sex workers) who are encouraged or forced to use drugs by drug dealers, pimps or both. The impact of drug rehabilitation and other treatment programs among particular groups is explored as well as the role of drug enforcement on the dynamics of this system. In particular, the roles of pimp pressure to use drugs, inability to quit due to addiction, and relapse from rehabilitation are explored. The effect of longer jail terms for drug leaders and pimps is discussed in the context of model and the data available.
Poster sessions award recipient at the National 2003 AMS convention in Baltimore, MD
BU-1619-M
BU-1620-M
BU-1621-M
BU-1622-M
BU-1623-M