Advances in Applied Probability

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

Frank Ball and David Sirl

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

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]

Coupling final outcome households local and global contacts multitype branching process multitype epidemic process multitype random graph threshold theorem


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.

Export citation