Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 44, Number 1 (2012), 63-86.
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 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.
Adv. in Appl. Probab., Volume 44, Number 1 (2012), 63-86.
First available in Project Euclid: 8 March 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 92D30: Epidemiology
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 05C80: Random graphs [See also 60B20]
Ball, Frank; Sirl, David. An SIR epidemic model on a population with random network and household structure, and several types of individuals. Adv. in Appl. Probab. 44 (2012), no. 1, 63--86. doi:10.1239/aap/1331216645. https://projecteuclid.org/euclid.aap/1331216645