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. Verhulsts 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. Lets 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_at_sbc.edu