Karen McCulloch

Doctor of Philosophy, (Mathematics)
Study Completed: 2017
College of Sciences


Thesis Title
An Analytical Approach to Modelling Epidemics on Networks

Read article at Massey Research Online: MRO icon

Understanding how infections can spread through different populations has important implications for control campaigns. Miss McCulloch used two types of epidemic models (SIR and SIS) to investigate the impact network topology has on the spread of an infection through a population. The probability mass functions of the final epidemic size of an SIR model for eight small networks of different topological structure were derived. She used results derived for the small networks to derive the final size probability mass function for a line of triangles network. The expected number of times each individual is infected during an epidemic and the expected time it takes for the infection to die out were derived for an SIS model on eight small networks. Her results illustrate how complex network epidemic models can be and contribute to the existing body of research that is aimed at determining exact epidemic results on finite networks.

Professor Mick Roberts
Professor Carlo Laing