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We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph representing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of individuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calculating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball et al. (2009) heuristically\ud motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results

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- (1995). A critical point for random graphs with a given degree sequence.
- (2002). A general model for stochastic SIR epidemics with two levels of mixing.
- (1986). A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models.
- (2010). Analysis of a stochastic SIR epidemic on a random network incorporating household structure.
- (2009). Analytical results for bond percolation and k-core sizes on clustered networks.
- (2003). Efficient immunization strategies for computer networks and populations.
- (2008). Epidemics on random graphs with tunable clustering.
- (1997). Epidemics with two levels of mixing.
- (2007). Graphs with specified degree distributions, simple epidemics, and local vaccination strategies.
- (1998). Limit theorems for a random graph epidemic model.
- (1971). Multitype branching processes. Theory and applications.
- (2008). Network epidemic models with two levels of mixing.
- (1972). On a certain model of an epidemic.
- (1972). On an epidemic in a stratified population.
- (2007). On analytical approaches to epidemics on networks.
- (2006). Optimal vaccination schemes for epidemics among a population of households, with application to variola minor in Brazil.
- (2007). Random graph dynamics.
- (2002). Random graph models of social networks.
- (2007). Second look at the spread of epidemics on networks.
- (2002). Spread of epidemic disease on networks.
- (2009). Spread of infectious disease through clustered populations.
- (2001). Stochastic multitype SIR epidemics among a population partitioned into households.
- (2000). Susceptibility sets and the final outcome of stochastic SIR epidemic models.
- (1999). The distribution of general final state random variables for stochastic epidemic models.
- (1995). The effect of household distribution on transmission and control of highly infectious diseases.
- (1998). The effect of random vaccine response on the vaccination coverage required to prevent epidemics.
- (2003). The great circle epidemic model. Stochastic Process.
- (2008). The relationship between real-time and discrete-generation models of epidemic spread.
- (2009). Threshold behaviour and final outcome of an epidemic on a random network with household structure.

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