Biomathematics: Developing a Textbook and Case Study Manual

1. Biomathematics: Developing a Textbook and Case Study Manual for Introductory Courses in Mathematical Biology (CCLI Award # 0340930) Raina Robeva, James Kirkwood, Robin Davies - Sweet Briar College, Sweet Briar, VA M. Johnson, B. Kovatchev – University of Virginia, Charlottesville, VA Major Objective To bridge the gap between graduate-level texts in biomathematics and the rigidly disciplinary preparation of undergraduates. Distinct Features • Written at a level that requires minimal mathematics and biology prerequisites; • Uses current research data that will heighten student interest and emphasize the idea that there may be several approaches to solving some problems; • Includes case studies that will provide independent, hands-on student projects designed to reinforce the chapter content and replicate the challenges of actual research experiences; • Teaches specific ways of thinking and problem solving skills that are often used in biomathematics; • Based (except for the introductory material) on current research projects at the Center for Biomathematical Technology at UVA. Invitation to Biomathematics (Under Contract from Elsevier with tentative publication date February 2007) Part 1. Core Concepts Chapter 1. Processes that Change with Time. Introduction to Dynamical Systems. Continuous and discrete dynamical population growth models. Unlimited growth. Verhulst’s logistic growth model. Population growth with delay. Physiological mechanisms of drug elimination. Introduction to Berkeley Madonna. Chapter 2. Complex Dynamics Emerging from Interacting Dynamical Systems. Interacting Populations - Continuous models governing the sizes of interacting populations. Infectious Diseases and Epidemiology - Epidemic models in a closed system: SIR, and SIS models, SIR with intermediate groups and delay. Predator-prey, competition, and symbiotic models. Chapter 3. Mathematics in Genetics Examine the dynamic of gene frequencies in a closed population. Hardy-Weinberg equilibrium. Disappearance of harmful alleles. Quantitative Genetics - Analysis of continuous traits and polygenic inheritance. “Why does human height have a Gaussian (Normal) distribution?”. Chapter 4.Quantitative Genetics and Statistics Examine the question of genetic inheritance. Determining the significance of an underlying genetic factor, relative to the contribution of environmental noise. Part 2. Let’s Do Research! Chapter 5. Risk Analysis of Blood Glucose Data. Quantitative approaches to diabetes control; Mathematical models for predicting severe hypoglycemia in diabetes. Chapter 6. Predicting Septicemia in Neonates. Predicting sepsis in prematurely born babies from heart rate data. Measures of irregularity in time series. Chapter 7. Cooperative binding, how your blood transports oxygen? Historical introduction to mathematical models describing hemoglobin-oxygen binding. Chapter 8. Data Fitting and Least Square Estimates of the Model Parameters Examine non-linear regression and goodness of fit in the context of hemoglobin-oxygen binding and enzyme kinetics.. Chapter 9. Endocrinology and Hormone Pulsatility. Pulsatile nature of hormone release; Peaks in hormone time series. Applications to treatment of infertility. Chapter 10. Endocrine network modeling. Feedback loops and hormone oscillations Network modeling of endocrine oscillators. Modeling and analysis of the growth hormone network. Chapter 11. Detecting Rhythms in Confounded Data Biological clocks. Circadian rhythms in confounded data. Some tools used to study rhythmic phenomena. Chapter 12. Circadian Gene Expression The use of microarrays for examining circadian gene expressions. www.biomath.sbc.edu Contact Information: Robeva@sbc.edu