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Epidemics on networks

Presented by: 
Frank Granville Ball University of Nottingham
Thursday 18th August 2016 - 14:00 to 15:00
INI Seminar Room 2
In this talk we consider two extensions of the standard stochastic epidemic SIR (Susceptible-Infected-Recovered) on a configuration model network.  The first extension, which is joint work with Peter Neal (Lancaster University), incorporates casual contacts, i.e. with people chosen uniformly at random from the population.  The second extension, which is joint work with Tom Britton (Stockholm University) and David Sirl (University of Nottingham), involves the spread of an epidemic on a random network model which allows for tunable clustering,  degree correlation and degree distribution.  For each model, approximating branching processes are used to obtain a threshold parameter, which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak, and the (approximate) probability and relative final size of a major outbreak.  For the model with casual contacts, an embedding argument is used to derive a central limit theorem for the size of a major epidemic; similar methods lead to the asymptotic variance of the giant component in a configuration model random graph.  The theory is illustrated by numerical studies, which explore the impact of network properties on the outcome of an epidemic.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons