Math 5110
Mathematical Biology I
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Fall term, 2007

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Professor Keener's home page
Math Biology Program
Department of Mathematics
University of Utah



Course Announcement

Math 5110 - Introduction to Mathematical Biology - I

Time: T,TH 12:25 - 1:45 pm

Place: LCB 225

Text:

L. Edelstein-Keshet, Mathematical Models in Biology. SIAM

TA: Lindsay Crowl, LCB 317. Office Hours: 2-4pm T, 1-3pm W.

The Course. Math 5110 is designed to introduce the mathematically apt to some of the basic models and methods of mathematical biology. To succeed in this class, you will need to have taken a course in linear algebra and ordinary differential equations. (Prerequisite for the course is Math 2250 or Math 2280.) No previous knowledge of biology is necessary.

The first semester covers models of population dynamics, reaction kinetics, diseases, and cells that can be written as ordinary differential questions, delay-differential equations, and discrete-time dynamical systems.

Homework:

Homework assignments will be posted and updated regularly here. Homework assignments will be due 1 week after they are assigned. Homework will account for 40% of your grade.

Homework 1: Problems due September 11, 2007

Homework 2: Problems due September 17, 2007

Homework 3: Problems due September 25, 2007

Homework 4: Problems due October 2, 2007

Homework 5: Problems due October 25, 2007

Homework 6: Problems due November 1, 2007

Homework 7: Problems due November 8,2007

Homework 8: Problems due November 29, 2007

Exams:

There willl be three takehome exams, two midterm and one final exam, each worth 20% of your grade.

Exam 1 (due Oct 4, 2007, 5pm)

Exam 2 (due Nov. 15, 2007, 5pm)

Final Exam (due Dec. 11, 2007, 5pm.)

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Course Outline (and Notes):

Extra readings are for students who are interested in learning more and pursuing the original literature, but are not required for the course. They are coordinated with the Mathematical Biology Journal Club.

Week of Topic Extra reading
August 20 Introduction to math biology
August 27 One dimensional maps PCR,population model code,data ,APD map [1]
September 3 Linear difference equations [2 ]
September 10 Systems of nonlinear equations [3]
September 17 Applications of systems Nicholson Bailey Matlab code Beddington Matlab code [4,5]
September 24 Formal intro to ODEs [6,7]
October 1 Midterm exam [8]
October 8 Harvesting theory [9,10]
October 15 Birth-death processes [11,12]
October 22 Delay differential equations [13,14]
October 28 The phase plane SIR DE matlab code,SIR DE RHS matlab code [15]
November 5 Chemostats and competitive exclusion Chemostat foodchain matlab code ,Chemostat RHS matlab code [16]
November 12 gene networks, biochemical Kinetics [17] [21]
November 19 Switches and cooperativity [18,19]
November 26 gene networks Lac operon Matlab code-pt I pt II [20]
December 3 excitability notes, circadian rhythms [20]

References

[1]
May, R. M. and Oster, G. Bifurcations and dynamic complexity in simple ecological models. American Naturalist 110, 573-599 (1976).

[2]
Leslie, P. H. On the use of matrices in certain population mathematics. Biometrika 33, 183-212 (1945).

[3]
Keener, J. P. On cardiac arrythmias: AV conduction block. Journal of Mathematical Biology 12, 215-225 (1981).

[4]
Nicholson, A. J. and Bailey, V. A. The balance of animal populations, part 1. Proceedings of the Zoological Society of London 3, 551-598 (1935).

[5]
May, R. M. Host-parasitoid systems in patchy environments: A phenomonological model. Journal of Animal Ecology 47, 833-844 (1978).

[6]
Clark, C. W. Mathematical Bioeconomics : the Optimal Management of Renewable Resources. Wiley, (1990).

[7]
Charnov, E. Optimal foraging: the marginal value theorem. Theoretical Population Biology 9, 129-136 (1976).

[8]
Ludwig, D., Jones, D. D., and Holling, C. S. Qualitative analysis of insect outbreak systems: the spruce budworm and forest. Journal of Animal Ecology 47, 315-332 (1978).

[9]
Kermack, W. O. and McKendrick, A. G. Contributions to the mathematical theory of epidemics. Royal Statistical Society Journal 115, 700-721 (1927).

[10]
Anderson, R. and May, R. M. Population biology of infectious diseases, part I. Nature 280, 361-367 (1979).

[11]
Bailey, N. The elements of stochastic processes. John Wiley and Sons, New York, (1964).

[12]
Pielou, E. C. Mathematical Ecology. John Wiley and Sons, New York, (1977).

[13]
Gurney, W. S. C., Blythe, S. P., and Nisbet, R. M. Nicholson's blowflies revisited. Nature 187, 17-21 (1980).

[14]
Mackey, M. C. and Glass, L. Oscillation and chaos in physiological control systems. Science 197, 287-289 (1977).

[15]
Volterra, V. Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560 (1926).

[16]
Armstrong, R. A. and McGehee, R. Competitive exclusion. American Naturalist 115, 151-170 (1980).

[17]
Briggs, G. E. and Haldane, J. B. S. A note on the kinetics of enzyme action. Biochemistry Journal 19, 338-339 (1925).

[18]
Pauling, L. The oxygen equilibrium of hemoglobin and its structural interpretation. Proc. Nat. Acad. Sci. 21, 186-191 (1935).

[19]
Monod, J., Wyman, J., and Changeux, J.-P. On the nature of allosteric transitions: a plausible model. Journal of Molecular Biology 12, 88-118 (1965).

[20]
Fitzhugh, R. Impulses and physiological states in theoretical models of nerve membranes. Biophysical Journal 1, 445-466 (1961).
[21]
J. J. Tyson, K. C. Chen, and B. Novak, Sniffers, buzzers, togles and blinkers: dynamcis of regulatory and signalling pathways in the cell Curr. Opinion in Cell Biology 15, 221-231 (2003).