Journal of Applied Probability

The probability of containment for multitype branching process models for emerging epidemics

Simon E. F. Spencer and Philip D. O'Neill

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Abstract

This paper is concerned with the definition and calculation of containment probabilities for emerging disease epidemics. A general multitype branching process is used to model an emerging infectious disease in a population of households. It is shown that the containment probability satisfies a certain fixed point equation which has a unique solution under certain conditions; the case of multiple solutions is also described. The extinction probability of the branching process is shown to be a special case of the containment probability. It is shown that Laplace transform ordering of the severity distributions of households in different epidemics yields an ordering on the containment probabilities. The results are illustrated with both standard epidemic models and a specific model for an emerging strain of influenza.

Article information

Source
J. Appl. Probab., Volume 48, Number 1 (2011), 173-188.

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1300198143

Digital Object Identifier
doi:10.1239/jap/1300198143

Mathematical Reviews number (MathSciNet)
MR2809894

Zentralblatt MATH identifier
1209.92055

Subjects
Primary: 92D30: Epidemiology
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching process epidemic influenza stochastic epidemic

Citation

Spencer, Simon E. F.; O'Neill, Philip D. The probability of containment for multitype branching process models for emerging epidemics. J. Appl. Probab. 48 (2011), no. 1, 173--188. doi:10.1239/jap/1300198143. https://projecteuclid.org/euclid.jap/1300198143


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