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An Sir Epidemic Model on a Population with Random Network and Household Structure, and Several Types of Individuals

  • Frank Ball (a1) and David Sirl (a1)

Abstract

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, Sirl and Trapman (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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Copyright

Corresponding author

Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: frank.ball@nottingham.ac.uk
∗∗ Current address: School of Mathematics, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK. Email address: d.sirl@lboro.ac.uk

References

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Keywords

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An Sir Epidemic Model on a Population with Random Network and Household Structure, and Several Types of Individuals

  • Frank Ball (a1) and David Sirl (a1)

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