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 Mathematics of Networks and Epidemics
Code MATH338
Coordinator Professor KJ Sharkey
Mathematical Sciences
K.J.Sharkey@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 6 FHEQ Second Semester 15

Aims

To develop expertise in networks and their applications, and in particular in mathematical biology.

Learning Outcomes

(LO1) Recognize networks in the real world and describe their mathematical representation.

(LO2) Classify networks, process them and calculate descriptive metrics for them.

(LO3) Analyse and asses idealised networks and their properties and evaluate how these conclusions relate to real world networks.

(LO4) Critical understanding of dynamics on networks and applications in biology, particularly in epidemics.

(S1) Problem solving skills

(S2) Numeracy

(S3) Programming in Matlab

Syllabus
 

Introduction: Examples of networks in the real works (Social, transport, internet, power grids, biochemical) and types of network (e.g. weighted, directed, hypergraph, bipartite, planar, trees).

Methods for characterising networks and their nodes: centrality measures, clustering, shortest paths, connected components and community detection.

Idealised networks: random graphs, degree distributions, configuration model, scale free, small world.

Network dynamics: percolation, giant component, epidemics on networks.

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):
MATH101 Calculus I; MATH221 Differential Equations 

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
Written exam  120    70       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework Assignment  60    30