Mathematical Biology & Ecology

Math 268A/CSYS 268A:  Spring 2018

  Meeting Times   T, R     1:15 - 2:30pm  in Votey 254
  Instructor   Prof. Daniel  Bentil
  Office   25 Colchester Avenue  (Mansfield House) Room 305
  Phone numbers   656 - 3832 (Office); 656 -2940 (Dept.)
  Text Mathematical Biology, Volumes I & II (3rd Edition): Murray, JD   (Required)

Mathematical Models in Biology: Edelstein-Keshet, L (Recommended)

  Material   Chapters will be covered based upon the topics outlined below
  Prerequisite   Prerequisite: Linear Algebra, Differential Equations, or Permission of Instructor
  Office Hours   Tuesdays 2:45 - 4:00pm
    Other times: By appointment only.
Homework & Projects 400 points 40%
Midterm Exam 300 points 30%
Final Project 300 points 30%
 Midterm Tests: 03/08/18; 04/12/18
Lectures & Guidelines

This course will be an introduction to the interplay of mathematics with several disciplines, namely biology, ecology, pharmacology and physiology, and it will be taught within the context of modeling complex systems. The applications we shall discuss will range from subcellular molecular systems and cellular behavior to physiological problems, chemical kinetics and population biology. No previous knowledge of these areas will be assumed. The biological background to each problem will be described in sufficient detail to construct and analyze models. The lectures will show how models of complex systems are built up and will provide the mathematical tools indispensable for studying their dynamics. With each topic discussed the scenario will consist of (i) a description of the biological problem; (ii) development of the mathematical model and an assessment of its realism; (iii) mathematical analysis of the model and clues to numerical computations; (iv) biological interpretation of the results from a modeling viewpoint. More specifically, a selection of modeling problems from the following areas will be studied:

I.   Continuous and  discrete models for interacting populations
II.  Reaction kinetics; Pharmacokinetic/Pharmacodynamic modeling
III. Biological wave phenomena; introduction to reaction diffusion theory
IV. Spatial pattern formation
V.  Dynamics of infectious diseases
VI. Seminal Papers & Project Work

We shall cover book chapters from Murray and allude to other topics (hand-outs to be provided) as may be required. The main emphasis of this course will be on techniques of mathematical modeling in biology and ecology, and in the context of mean-field type modeling of complex systems (not agent-based modeling of complex systems). Practical implementation of algorithms on computers will be encouraged.

Students with Special Needs: Students with documented learning disabilities are entitled by law to certain “reasonable accommodations.” If you have a documented reason for special accommodations, you must provide written evidence of this as soon as possible from the appropriate office. No accommodations can or will be given without the requisite documentation.

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