An SIR epidemic model on a population with random network and household structure and several types of individuals
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...
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| Format: | Article |
| Published: |
Applied Probability Trust
2010
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| Online Access: | https://eprints.nottingham.ac.uk/1393/ |
| Summary: | 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
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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