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Summer 2006
The Effects of Myeloid Cells on Tumor-Immune System Interaction in Different Time Scales
Diego Chowell, Facultad de Ciencias
Irina Kareva, University of Maryland
Rosa Torre, Cornell University
Anuj Mubayi, Arizona State University
Fabio Sánchez, Cornell University
Faina Berezovskaya, Howard University
MTBI-03-01M
Abstract: Despite the highly developed mechanism of the immune response, tumor cells often continue to grow uncontrollably. The recognition of tumor cells by specific immune cells is dependent on the balance between immature (ImC) and mature (MmC) myeloid cells in the body, a fact not widely used in tumor growth dynamics models. We propose a mathematical model that incorporates various stages of immune response to tumor growth. Our model includes the dynamics and interactions of tumor cells, natural killer cells, CD8+T cells, immature and mature myeloid cells. The resulting model is given by a five-dimensional non-linear system, which is reduced to a two-dimensional system using time-scale arguments and explored analytically. A discussion on the role of the ratio of immature to mature myeloid cells concludes our presentation.
An Epidemiological Approach to the Dynamics of Chytidiomycosis on a Harlequin Fog Population
Mario Antonio Ayala - Valenzuela,
Universidad de Colima
Casandra Leann Pawling, Arizona State University
Adrian Nicholas Smith, University of Washington
Linda Gao, North Central College
David Hiebeler, University of Manie
Benjamin Richard Morin, Oregon State University
MTBI-03-02M
Abstract: Amphibious species around the world are experiencing catastrophic decline and extinction. Chytridiomycosis, a newly recognized emerging infectious disease, is now thought to be a major contributor to observed rapid decline. Chytridiomycosis is a skin disease caused by the Chytrid fungus, a water-borne pathogen prevalent in Neotropical habitats. The Harlequin Frog, Atelopus Varius, native to the montane regions of Costa Rica, is one of the hundreds of species threatened by this epidemic disease. We study the dynamics of this host-pathogen system in a spatial-explicit setting. In order to gain qualitative understanding on the nature of this system, we conduct a mean field approximation, pair approximation, and computer simulation.
Estimation of Within-Host Reproductive Number Distributions from HIV-1 Viral Load Data
Jennifer Lamb, North Kentucky
University
Aníbal Y. López-Correa, University of Puerto Rico-Cayey
Kamau Romero, Brown University
Xiaohong Wang, Arizona State University
Ariel Cintron-Arias, Arizona State University
MTBI-03-03M
Abstract: The basic reproductive number R0 is defined as the expected number of secondary cases generated by a "typical" infected individual in a totally susceptible population. In the context of within-host viral dynamics, we study the reproductive number of virions and infected cells. In this study we utilize empirical data from ten anti-retroviral, drug-naive, patients infected with HIV-1, published by Stafford et. al. [18]. We apply a Bayesian procedure which results in the estimation of the full probability distribution of R0, due to Bettencourt and Riberiro. In addition, an uncertainty and sensitivity analysis of R0 is employed to assess the role played by variation of modell parameters in within-host viral dynamics.
The Impacts of the Sleeper Effect and Relapse on the Dynamics of Cigarette Smoking Among Adolescents
Odalys Colon-Rentas, University of
Puerto Rico
Leonard Gordon, Berea College
Ludguier D. Montejo, Columbia University
Pamela Reitsma, Whitman College
Fabio A Sánchez, Cornell University
Baojun Song, Montclair State University
MTBI-03-04M
Poster sessions award recipient at the National 2006 SIAM Conference on the Life Sciences in Raleigh, NC
Abstract: The Center for Disease Control (CDC) predicts that 6.4 million of today's children will die prematurely from a smoking related illness if environmental conditions remain the same. The percentage of high school students who smoke cigarettes has remained at around 23% for the past three years. Recent research reports a "sleeper effect" in children. That is, children who smoked once before age 11 are twice as likely to become a regular smoker by age 14. We model smoking dynamics among children ages 11 to 18 as a "socially-transmitted" disease, and use it to explore possible mechanisms of the "sleeper effect." Is it due to prior exposure or is it due to higher relapse rates? The model fits the number of smokers for the past 16 years as reported by the CDC. The feasibility of the CDC's goal for 2010 is evaluated. The significance of relapse is highlighted by a simple bifurcation analysis. The effects of education on this group are explored and recommendations for effective approaches are made.
A theoretical framework for a three-state spatial population model with applications
Michelle Bettelheim, Columbia University
Jennifer Houle, University of Maine
Fabian Librado, University of Idaho
David Hiebeler, University of Maine
Karen R. Ríos-Soto, Cornell University
MTBI-03-05M
Abstract: The theoretical work of this presentation is motivated by our efforts to understand spatial-temporal dynamics of biological systems whose main features can be roughly captured by three states. The general model is constructed and approximate sub-models used to help increase (eventually) our understanding of the dynamics of three-state systems. The pair approximation method is used to construct a spatial sub-model with nearest neighbor interaction. The spatially implicit mean field approximation of the three-state model is also investigated to study the dynamics of the null-model, that is the dynamics of a model without the spatial component. Dynamics of our approximation are compared with a stochastic computer simulation (based on continuous time Poisson processes) of the full model. The reliability of the pair approximation and the mean field model is discussed. The model is applied to the protection of crops against infestation and the spread of influenza in a closed environment with temporary vaccination.
Mathematical Modeling of the Sex Worker Industry as a Supply and Demand System
Lily Davidoff, New Jersey Institute of
Technology
Karyn Sutton, Arizona State University
Genevieve-Yvonne Toutain, Arizona State University
Fabio Sánchez, Cornell University
Christopher Kribs-Zaleta, University of Texas at Arlington
Carlos Castillo-Chavez, Arizona State University
MTBI-03-06M
Abstract: Prostitution is an occupation of global presence, often referred to as the worlds oldest, having existed for millennia. In the United States, the estimated annual prevalence of full-time sex workers is approximately 23 per every 100,000 individuals in the population. We construct two mathematical models to explore the dynamics of the sex industry: one for the males who provide demand and another for the females who provide the supply. We perform qualitative analysis on these models separately, and explore the coupled system numerically. Through this analysis, we provide possible explanations as to why the current system of arrest and detainment does little to control the sex worker population. In addition, we show that if the efforts of legal enforcement focus on making male arrests, it is possible to significantly reduce the number of women in prostitution.
OCD Therapeutic Dynamics: Markovian Based Simulations
Ricardo Cordero-Sodo, Universidad
Metropolitana
Karla Hernandez, Universidad de Colima
Daniel Ríos-Doria, CUNY College of Staten Island
Kehinde Salau, St. Mary's College of Maryland
Christopher Kribs Zabeta
David Murillo, Arizona State University
MTBI-03-07M
Abstract: Up to 3 percent of the population suffers from a mental disorder known as Obsessive-Compulsive Disorder(OCD). Although full understanding of this disorder still eludes scientists, there is a general consensus on district methods of treatment including Selective Serotonin Re-uptake Inhibitors, various types of group therapy, and individual therapy. This paper uses finite Continuous Time Markov Chains (CTMC) to model the treatment dynamics of Obsessive-Compulsive individuals. The models proposed herein include factors such as access to group or individual therapy and health insurance constraints, and are modified to include prescribed treatment regimens. Naturally, added realism moves out of the "neatness" inherent in CTMC models. Realistic extensions in the CTMC models are therefore addressed by numerical means (simulations). To minimize time and cost, we establish necessary conditions between the recruitment rate of individual therapy and the recruitment rate for the group therapy. These conditions depend on the magnitude of the recovery rate for group therapy.