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

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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.

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 1 (2012), 63-86.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1331216645

Digital Object Identifier
doi:10.1239/aap/1331216645

Mathematical Reviews number (MathSciNet)
MR2951547

Zentralblatt MATH identifier
1236.92043

Subjects
Primary: 92D30: Epidemiology
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 05C80: Random graphs [See also 60B20]

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

Citation

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


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