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This paper considers a stochastic SIR (susceptible→infective→removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process… (More)

- Frank Ball, David Sirl, Pieter Trapman
- Mathematical biosciences
- 2010

This paper is concerned with a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A… (More)

In this paper we consider a model for the spread of a stochastic SIR (Susceptible → Infectious → Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of cliques, each of random size, and infection can be transmitted between two individuals if and only if there is a clique they both… (More)

- Joshua V Ross, David J Sirl, Philip K Pollett, Hugh P Possingham
- Ecological applications : a publication of the…
- 2008

Habitat loss and fragmentation has created metapopulations where there were once continuous populations. Ecologists and conservation biologists have become interested in the optimal way to manage and conserve such metapopulations. Several authors have considered the effect of patch disturbance and recovery on metapopulation persistence, but almost all such… (More)

- Frank Ball, David Sirl
- J. Applied Probability
- 2013

- Frank Ball, Tom Britton, David Sirl
- Journal of mathematical biology
- 2013

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree… (More)

- David Sirl
- 2004

Quasistationary Distributions for Continuous-Time Markov Chains – p.1

- David Sirl
- 2004

- Frank Ball, David Sirl
- Journal of mathematical biology
- 2017

This paper is concerned with the analysis of vaccination strategies in a stochastic susceptible [Formula: see text] infected [Formula: see text] removed model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also partitioned into households. Under various vaccine action models, we consider… (More)

- Frank Ball, Tom Britton, David Sirl
- Journal of mathematical biology
- 2011

This paper is concerned with SIR (susceptible → infected → removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to… (More)

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