Instructor: Dr. T. Hillen,

CAB 575, thillen@ualberta.ca , 492-3395

Outline:

This course will cover the following material

1. Introduction (3 lectures)

• Review: Predator Prey Models

• Parameter Estimations

2. Reaction Kinetics (3 lectures),  [J. Keener, J. Sneyd]

• Michaelis-Menten Kinetics

• Singular Perturbation Theory

• Examples

3. Sojourn Time Analysis (6 lectures), [H. Thieme]

• Definition, Expected Life Time, Variance

• Remaining Sojourn Times

• Mortality Rates and Exit Rates

• Stage Dynamics with Given Input

• Partial Differential Equation Formulation

• Some Nonlinear Demographics

4. Models for Radiation Treatment of Cancer (4 lectures)

• The linear quadratic model (LQ-Model)

• The LPL model  and the Leah-Catchside Protraction Factor

• Tumor Control Probability (TCP)

• TCP from a simple Cell Cycle Model (with A. Dawson and O. Yurtseven)

 5. Spatially Explicit Population Models using Reaction-Diffusion Equations (4 lectures)

• Derivation [ sec. 4.3.1 in de Vries et al]

• Fundamental Solution [sec. 4.3.2 in de Vries et al]

• Critical Domain Size Problem [sec. 4.3.3 in de Vries et al]

• Using the Hamiltonian to calculate l*

• Traveling Waves 

• Epidemic Waves

6. Pattern Formation (4 lectures)

• Turing patterns

• Chemotaxis:  Individual and population measurements, a 1-D hyperbolic model, 

• The classical chemotaxis model 

• Regularizations

7. Transport Equations

Prerequisites: Some basic knowledge on PDE’s.

Research Project:

Each student will be given a research project to work on during the entire term.

1. The first homework is to find a good research project for this term. Please hand in a written 2-page description of your planned project by Jan 19, 2006 in class.

2. (Midterm 30%) On Feb 16, 2006 your research proposal is due. Please give a short 10-15 minute presentation and a 3-4 page research proposal. This means, please include the sections:Title, Abstract, Background, Purpose of the Research Project, Methods and Proposed Approach, Time Plan. Assume I am a granting agency and try to convince me that I should invest lots of money into your project. 

3. (Final 50%) on April 26, 10 AM in CAB 567: each student will hand in a written documentation (about 6 pages) of his/her project work and give a 20 minute presentation.

Grading:

Homework assignments 20 %, there will be irregular homework assignments.  

Midterm: research proposal and  project presentation: 30%,

Final project manuscript and presentation: 50%

Textbook(s): (no textbooks are required)

•  Britton, Essential Mathematical Biology, Springer, 2003

• Cantrell and Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley,  

• de Vries, Hillen, Lewis, Müller, Schönfisch A Course In Mathematical Biology, SIAM, 2006.

• Murray I and II, Mathematical Biology, Springer 2003.

• Thieme, Mathematics in Population Biology, Princeton Univ. Press, 2003

• See a reference list of textbooks at the end of de Vries et al.