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{1300198143,
author = {Spencer, Simon E. F. and O'Neill, Philip D.},
title = {The probability of containment for multitype branching process models for emerging epidemics},
journal = {J. Appl. Probab.},
volume = {48},
number = {1},
year = {2011},
pages = { 173-188},
language = {en},
url = {http://dml.mathdoc.fr/item/1300198143}
}
Spencer, Simon E. F.; O'Neill, Philip D. The probability of containment for multitype branching process models for emerging epidemics. J. Appl. Probab., Tome 48 (2011) no. 1, pp. 173-188. http://gdmltest.u-ga.fr/item/1300198143/