Module Code - Title:
MA6012
-
MATHEMATICAL BIOLOGY AND PHYSIOLOGY
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
Prerequisite Modules:
Rationale and Purpose of the Module:
Syllabus:
Stability
Continuous population models: stability, bifurcations.
Hysteresis, non-dimensionalisation.
Discrete models: stability, chaos. Harvesting: optimal strategies.
Oscillations
Lotka-Volterra model.
Predator-prey systems. Limit cycles.
Enzyme reactions
Michaelis-Menten kinetics: pseudo-steady state hypothesis.
Allosteric enzymes.
Glycolysis. Glycolytic oscillations. Calcium dynamics.
Waves
Fisher equation.Excitable media.
Signal propagation in nerve cells. Hodgkin-Huxley model.
Pattern formation
Reaction-diffusion.Turing instability. Spiral waves. Cardiac instability.
Respiratory control.
The Mackey-Glass model. The Grodins model.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
1. Develop the ability to build mathematical models for biological and physiological systems involving o.d.e.s, p.d.e.s and delay differential equations.
Final exam and homework for credit.
2. Learn biological principles necessary to model-building, including enzyme kinetics, calcium signalling, respiratory physiology.
Final exam and homework for credit.
3. Understand principles of non-dimensionalisation, travelling wave and stability theory, phase plane analysis, singular perturbation theory, and their applications.
Final exam and homework for credit.
4. Understand model applications in population dynamics, enzyme kinetics, cardiac dynamics, respiration.
Final exam and homework for credit.
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Keener, J. and Sneyd, J., (2001)
A mathematical physiology (2e)
, Springer
Guyton, A.C. and Hall, J. E (2005)
Textbook of medical physiology (11e)
, W. B. Saunders Co., Philadelphia
Other Relevant Texts:
Glass, L. and Mackey, M.C. (1988)
From clocks to chaos
, Princeton University Press
Murray, J.D. (1993)
Mathematical biology (2e)
, Springer-Verlag
Hoppensteadt F., (1975)
Mathematical theories of populations: demographics, genetics and epidemics
, SIAM, Philadelphia
Segel, L.A. (1984)
Modeling dynamic phenomena in molecular and cellular biology
, Cambridge University Press
Rubinow, S.I. (1975)
Introduction to mathematical biology
, John Wiley
Goldbeter, A (1996)
Biochemical oscillations and cellular rhythms
, Cambridge University Press
Renshaw, E. (1991)
Modelling biological populations in space and time
, Cambridge University Press
Drazin, P.G., (2008)
Nonlinear systems
, Cambridge University Press.
Jordan, D.W. and Smith, P., (2007)
Nonlinear ordinary differential equations (4e)
, Oxford University Press
Grindrod, P (1991)
Patterns and waves
, Oxford University Press
Berne, R.M., and Levy, M.N. (1996)
Principles of physiology (2e)
, Mosby, St. Louis
Levick, J.R (2000)
An introduction to cardiovascular physiology (3e)
, Butterworth-Heinemann, Oxford
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
Andrew.Fowler@ul.ie