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, Robin Davies, James Kirkwood - Sweet Briar College, Sweet Briar, VA B. Kovatchev, M. Johnson, M. Straume, L. Farhy – University of Virginia, Charlottesville, VA Major Objective Bridge the gap between graduate-level programs in biomathematics and the rigidly disciplinary preparation of undergraduates. Distinct Features • written at a level that requires minimal mathematics and biology prerequisites; • use current research data that will heighten student interest and emphasize the idea that there may be several approaches to solving some problems; • include case studies that will provide independent, hands-on student projects designed to reinforce the chapter content and replicate the challenges of actual research experiences; • teach specific ways of thinking and problem solving skills that are often used in biomathematics; and • based (except for the introductory material) on current research projects at the Center for Biomathematical Technology at UVA. Biomathematics (Under Contract from Elsevier Press) Chapter 0. The Place of Biomathematics in Contemporary Life Science Research. Outline of research trends at the frontier of the life sciences benefiting from biomathematics analyses. Part 1. Back to the Basics Chapter 1. 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; Predator-prey, competition, and symbiotic models; Infectious Diseases and Epidemiology - Epidemic models in a closed system: SIR, and SIS models, SIR with intermediate groups and delay. Chapter 3. Population and Quantitative Genetics. Selection 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. Cooperative binding, how your blood transports oxygen? Examine non-linear regression and goodness of fit in the context of hemoglobin-oxygen binding and enzyme kinetics models. Part 2. Let’s Do Research! Chapter 5. Endocrinology and Hormone Pulsatility. Pulsatile nature of hormone release; Peaks in hormone time series; Applications to treatment of infertility. Chapter 6. Modeling of Hormone Feedback Networks. Network modeling of endocrine oscillators; Modeling and analysis of the growth hormone network. Chapter 7. Do Humans Grow Stepwise? Saltation and stasis in normal human development; Mathematical modeling of growth. Chapter 8. Circadian Rhythms and Periodicity. Circadian rhythms; Rhythm analyses of confounded time series; Scheduling of cancer radio/chemotherapy. Chapter 9. Gene Chips and Biological Clocks. Genes and biological clocks; Extremely large time series data sets; Empirical statistical (resampling) methodologies. Chapter 10. Predicting Septicemia in Neonates. Predicting sepsis in prematurely born babies from heart rate data; Measures of irregularity in time series; Risk functions and indices. Chapter 11. Risk Analysis of Blood Glucose Data. Quantitative approaches to diabetes control; Mathematical models for predicting severe hypoglycemia in diabetes. www.biomath.sbc.edu Contact Information: Robeva@sbc.edu