MA800 Mathematical biology

Instructor: Nikolay S. Strigul

E-mails: nstrigul@stevens.edu, nstrigul@princeton.edu

Office Hours: by appointment

Lectures: Tuesdays 06:15-08:45 pm, Kidde 228.

Homeworks: There will be weekly homework assignments.

Exams: There will be Midterm and Final Exams.

Grading:

- Homework assignments: 30 %

- Midterm: 30 %

- Final: 40 %

Course programCourse announcement (PDF) Course program (PDF)

General comments:This course targets students majoring in both computational and biological sciences, broadly defined to include mathematical, computer science, bio-medical and environmental majors. The goal of this course is to give students an understanding of the biological-mathematical interface, and how mathematics contributes to the study of biological phenomena. Biological systems have a very high level of complexity and practically every phenomenon is the result of complex interactions between various levels of organization. To apply modeling (both mathematical and experimental models), we always simplify the natural system by making both implicit and explicit assumptions, and this course teaches students to see the hidden assumptions and understand their role in the results of model applications.

The course introduces general mathematical methods in biology, such as scaling, approximations of stochastic and individual-based biological models by differential equations, and linearization and stability analysis, using both classic and recent examples. The course covers fundamental and applied models operating at different organization levels, from processes inside individual cells to those that form ecosystems. Specific examples include: dynamics of infectious diseases (flu epidemics and AIDS), natural recourse management (fisheries), forest dynamics, interacting species (resource competition, predator-prey, and host-parasite models), spatial models, enzyme kinetics, chemostat theory, and bioremediation. In this course biology students learn to formulate their specific questions in a mathematical way, while mathematics students learn what constitutes biologically relevant questions, and how to accept the high level of uncertainty that exists in biological research. A substantial part of the course will use analytical methods in concert with computer simulations, using the Mathematica software.Textbooks:

1) L. Edelstein-Keshet. Mathematical Models in Biology. 2005 ISBN: 0898715547

2) A.Hastings. Population Biology: Concepts and Methods. 1997 ISBN 0-387-94862-7

3) A. Okubo, S.A. Levin. Diffusion and Ecological Problems. 2002 ISBN: 0387986766

4) J.D. Murray. Mathematical Biology I. 2005 ISBN: 0387952233

5) M. Kot. Elements of Mathematical Ecology. 2001 ISBN: 0521001501

6) S.A. Levin. Theoretical Biology. (unpublished lecture notes) 2005. Princeton University (used with permission)

Acknowledgement:

I would like to thank Professor Simon Levin for his advice and the permission to use unpublished materials from his course "Theoretical Biology".

Course program:Lecture 1.- Introduction: biological systems as complex adaptive systems. Discrete and continuous single species models.

Lecture 2.- Age- and size- structured populations. Natural resource management, fisheries.

Lecture 3.- Enzyme kinetics.

Lecture 4.- Microbiological models: biodegradation and chemostat theory.

Lecture 5.- Multi-species communities I. Competition models, coexistence.

Lecture 6.- Multi-species communities II. Predator-prey models. Optimal foraging.

Lecture 7.- Multi-species communities III. Host-parasite dynamics.

Lecture 8.- Infectious diseases I. SIR models.

Lecture 9.- Infectious diseases II. Flu epidemics, AIDS.

Lecture 10.- Spatially-distributed models I. Conservation equation.

Lecture 11.- Forest modeling.

Lecture 12.- Spatially-distributed models II. Random walk and diffusion. Fick's laws.

Lecture 13.- Spatially-distributed models III. Diffusion in biological settings.

Lecture 14.- Fitting models to data. Optimal experimental designs.

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