Resources
Intended Learning Outcomes
Once you've successfully completed this module you should be able to:
 Interpret differential equation models for populations, relating the expressions appearing in the model to processes
that affect the population.
 Formulate and analyse ordinary differential equation (ODE) models for the population of a single species, finding
equilibrium populations and determining how their stability depends on parameters.
 Analyse delaydifferential equation (DDE) models for the population of a single species and use linear stability
analysis to determine which values of the parameters induce oscillatory instabilities.
 Analyse ODE models for the populations of two interacting species, finding equilibria and using information about their
linear stability to characterise the longterm behaviour of the system.
 Define a conserved quantity for a system of ODEs and, where possible, use such quantities to determine the
longterm behaviour of both twospecies ODE models and singlespecies models population models that include diffusion.
 Construct the ODEs associated with a system of chemical reactions subject to massaction kinetics and analyse them to
discover conserved quantities.
 Construct the Markov process associated with a system of chemical reactions and, for small numbers of reactions,
analyse it to determine the longterm behaviour of the system.
 Analyse two key models, Wolpert's Frech flag model and Turing's reactiondiffusion model, relating the
solutions of the associated PDEs to the processes of patternformation in developing organisms.
Lecture Notes and Articles
The first half of the course will cover classical topics in mathematical biology, following sections of Jim Murray's famous text,
Mathematical Biology I: An Introduction. This book is available online
from within the University's network. For offcampus access, you can install software that will allow you to use all the Library's services via the
University's Virtual Private Network (VPN).
Lecture notes will appear here.
Opportunities for feedback
The main channel for formal, written feedback in this module is the coursework. It will be a problem set similar
to the ones provided on this page, but devoted to a novel application that uses the ideas from the course. You'll prepare written solutions
and I'll mark them over the Easter Break, providing both written comments and a mark. In addition, the weekly examples classes
provide further opportunities for verbal feedback and, for students who bring written solutions to the
exercises, onthespot marking and written feedback as well.
Problem Sets & Solutions
Problem sets will be released throughout the course and will appear here

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Coursework
The coursework will be due at 3:00 PM on Monday, 29 April. The coursework contributes 20% to your final mark for the module and will be marked out of 20. Potential topics: generation of nerve impulses; firefly synchronization; temperature control of circadian clocks
Week 3 Questionnaires
Watch here for a brief summary of and response to the Week 3 questionnaires
Coursework & Exams
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Background reading
A hyperlinked version of the lists below is available from Manchester University
Library's Link2Lists system.
For key mathematical ideas and techniques:
 James D. Murray, Mathematical Biology I: An Introduction 3rd edition, (Springer, 2002).
ISBN 0387952233
 James D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications 3rd edition, (Springer, 2002).
ISBN 0387952284
 Lee A. Segel, Modeling dynamic phenomena in molecular and cellular biology (Cambridge University Press, 1984).
ISBN 052127477X
 Darren J. Wilkinson, Stochastic Modelling for Systems Biology (Chapman & Hall/CRC, 2006).
ISBN 1584885408
For biological background:
 Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts and Peter Walter (2002)
Molecular Biology of the Cell. 4th edition, Garland Science. ISBN 0815340729
 Uri Alon (2008) An Introduction to Systems Biology: Design Principles of Biological Circuits
(Chapman & Hall/CRC, 2007). ISBN 1584886420
 Terry A. Brown (2007) Genomes 3. Garland Science. ISBN 0815341385
The previous edition,
Genomes 2, is available online
from the National Center for Biotechnology Information (NCBI) Bookshelf
 Eric H. Davidson (2006) The Regulatory Genome. Academic Press. ISBN 0120885638
 Evelyn Fox Keller (2002) Making Sense of Life,
Harvard University Press. ISBN 067401250X
 Edda Klipp, Wolfram Liebermeister, Christoph Wierling, Axel Kowald, Hans Lehrach, Ralf Herwig (2009)
Systems Biology: A Textbook. WileyBlackwell. ISBN 9783527318742
 Bernhard Ø. Palsson (2006) Systems Biology: Properties of Reconstructed Networks. Cambridge University Press. ISBN 0521859034
 Ron Milo, Rob Philips (2016) Cell Biology by the Numbers. Taylor & Francis. ISBN 9780815345374
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