Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Advanced topics in mathematical biology
Code MATH426
Coordinator Dr CE Overton
Mathematical Sciences
C.Overton@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 7 FHEQ First Semester 15

Aims

To introduce some hot problems of contemporary mathematical biology, including analysis of developmental processes, networks and biological mechanics.

To further develop mathematical skills in the areas of difference equations and ordinary and partial differential equations.

To explore biological applications of fluid dynamics in the limit of low and high Reynolds number.

Learning Outcomes

(LO1) Understand mathematical modelling methodology used in contemporary mathematical biology.

(LO2) Be able to use techniques from difference equations and ordinary and partial differential equations in tackling problems in biology.

Syllabus
 

Weeks 1-4: Biological fluid dynamics: low Re flow - flow field around sphere (sinking speed of marine particles, hydrodynamic signalling, circulation, lift, drag); high Re flow (inviscid flow), steady flight (Bernoulli's theory, Kutta-Joukowski hypothesis, circulation, lift, drag)

Weeks 5-8: Epidemic dynamics on Networks: introduction to epidemic models on graphs, particularly Markovian SIS and SIR dynamics;  overview of recent results and methods (e.g. pair-approximation, long-term behaviour of the dynamics)

Weeks 9-12: Modelling developmental processes: cell-cell signalling and cellular differentiation in biological tissues; scaling of biological patterns, noise and fluctuations in biological systems; movement of cells in tissues.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH102 CALCULUS II; MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH102 CALCULUS II 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment  90    50       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 3  0    10       
Homework 1  0    20       
Homework 2  0    20