David Sirl

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

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 threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

THRESHOLD BEHAVIOUR AND FINAL OUTCOME OF AN EPIDEMIC ON A RANDOM NETWORK WITH HOUSEHOLD STRUCTURE

In this paper we consider 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 approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly sized finite populations. The extension to unequal-sized households is discussed briefly.

Epidemics on random intersection graphs

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. In ...

A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon

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 correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible

An SIR epidemic model on a population with random network and household structure and several types of individuals

\rightarrow

Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure

Infective

Individual preventive social distancing during an epidemic may have negative population-level outcomes

\rightarrow