EXACT ANALYTICAL EXPRESSIONS FOR THE FINAL EPIDEMIC SIZE OF AN SIR MODEL ON SMALL NETWORKS
K Mcculloch, MG Roberts, CR Laing
ANZIAM JOURNAL | CAMBRIDGE UNIV PRESS | Published : 2016
We investigate the dynamics of a susceptible infected recovered (SIR) epidemic model on small networks with different topologies, as a stepping stone to determining how the structure of a contact network impacts the transmission of infection through a population. For an SIR model on a network of nodes, there are configurations that the network can be in. To simplify the analysis, we group the states together based on the number of nodes in each infection state and the symmetries of the network. We derive analytical expressions for the final epidemic size of an SIR model on small networks composed of three or four nodes with different topological structures. Differential equations which descr..View full abstract
Awarded by Marsden Fund
This research was supported by the Marsden Fund (MAU1106), which we acknowledge and thank for their support. We also wish to thank Dr Roslyn Hickson for helping with the Gillespie algorithm code and for many insightful discussions.