B5.5 Further Mathematical Biology - Material for the year 2020-2021

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2020-2021
Lecturer(s): 
Prof. Ruth Baker
General Prerequisites: 

Part A Differential Equations I and Modelling in Mathematical Biology. Part A Differential Equations II is also preferable but not necessary.

Course Term: 
Michaelmas
Course Lecture Information: 

16 lectures

Course Weight: 
1.00 unit(s)
Course Level: 
H

Assessment type:

Course Overview: 

Further Mathematical Biology provides an introduction to more complicated models of biological phenomena, including spatial models of pattern formation and free boundary problems modelling invasion. The course focuses on applications where continuum, deterministic models formulated using ordinary and/or partial differential equations are appropriate, but also includes an introduction to discrete, stochastic models and how to relate them to continuum models. By using particular modelling examples in ecology, chemistry, biology and physiology, the course demonstrates how applied mathematical techniques, such as linear stability, phase planes and travelling waves, can yield important information about the behaviour of complicated models.

Learning Outcomes: 

Students will have developed a sound knowledge and appreciation of the ideas and concepts related to modelling biological and ecological systems using ordinary and partial differential equations and been introduced to discrete stochastic models.

Course Synopsis: 

Enzyme-substrate kinetics, the quasi-steady state approximation and perturbation analysis.

Age-structured models with biological and physiological examples.

Introduction to spatial models, including morphogen gradients, chemotaxis and patterning.

Travelling wave propagation with biological examples, including Fisher’s equation and epidemics.

Biological pattern formation, including Turing's model for animal coat markings and chemotaxis models.

Moving boundary problems with biological examples, including colonisation and wound healing.

Discrete-to-continuum models, including space- and velocity-jump models for diffusion and chemotaxis.

Reading List: 
  1. J.D. Murray, Mathematical Biology, Volume I: An Introduction, 3rd Edition (Springer, 2002).
  2. J.D. Murray, Mathematical Biology, Volume II: Spatial Models and Biomedical Applications, 3rd edition (Springer, 2003).
  3. L. Edelstein-Keshet, Mathematical Models in Biology. (SIAM, 2005)
Further Reading: 
  1. J. Keener and J. Sneyd, Mathematical Physiology (First Edition Springer, Berlin, 1998)
  2. N. F . Britton, Essential Mathematical Biology (Springer, London, 2003).
  3. H. G. Othmer, S. R. Dunbar and W. Alt, Models of dispersal in biological systems. Journal of Mathematical Biology, 26:263-298 (1988).