Mathematical Biology I

Course Description

Textbook

Reference Books

Gillespie, J.H. Population Genetics: A Concise Guide. The Johns Hopkins Univ. Press, Baltimore, MD, 1998. [QH455 .G565 1998]

Hertz, J., Krogh, A., and Palmer, R.G. Introduction to the Theory of Neural Computation. Addision-Eesley Publish Co., Redwood, CA, 1991. [QA76.5 .H475 1991]

Hoppensteadt, F.C. An Introduction to the Mathematics of Neurons. 2nd Edition, Cambridge University Press, London, 1997. [QP363.3 .H67 1997]

Keener, J. and Sneyd, J. Mathematical Physiology. Springer-Verlag, New York, 1998. [QT 35 K26m 1998]

Murray, J.D. Mathematical Biology II: Spatial Models. 3rd Edition, Springer, New York 2002. [QH323.5 .M88 2002 v.2]

Segel, I.H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. John Wiley & Sons, New York, 1975. [QU 135 S454e 1975]

Syllabus

(1) Review of Ordinary Differential Equations: Mechanics, population dynamics, chemical kinetics: fundamental laws and constitutive relations.

(2) Continuous Population Dynamics: single species, bifurcation, and stability (Ch.1).

(3) Delay Models.(Ch.1)

(3.1) Additional Reading: On DDE

(4) Continuous Interacting Population Models. (Ch.3)

(5) Discrete Population Models: logistic model, bifurcation to chaos (Ch.2).

(6) Mendelian Population Dynamics: allel frequency and relation to simple population dynamics

(6.1) Additional Reading: more on population genetics

(7) Enzyme Kinetics: Michaelis-Menten theory, rapid pre-equilibrium and pseudo-steady state, singular perturbation (Ch.6).

(7.1) Additional Reading: stochastic modeling of kinetics

(7.2) Additional Reading: kinetics at high enzyme concentration

(8) Simple Oscillatory Reactions. (Ch.6)

(9) Hodgkin-Huxley Theory. (Ch. 6)

(10) Discrete, Continuous, and Delay Neural Networks.

(10.1) Additional Reading: stochastic resonance

(11) Belousov-Zhabotinskii Reaction. (Ch. 7)

(11.1) Additional Reading: existence of limit cycle

(12) Coupled Oscillators. (Ch. 8)

(13) More on Coupled Oscillators. (Ch. 9)

(14) Reaction Diffusion Equation. (Ch. 11)

(15) Biological Waves from Single Species. (Ch. 13)

(16) Reaction-Diffusion Approach to Cellular Mechanics.

(16.1) Additional Reading: one-dimensional diffusion problems

(17) Dynamics of Infectious Diseases (Ch. 13)

(17.1) Additional Reading: infectious disease coupled with evolution