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The Daniels' Poisson limit theorem for the final size of a severe general stochastic epidemic is extended to the Martin-Löf epidemic, and an order of magnitude for the error in the approximation is also given. The argument consists largely of showing that the number of survivors of a severe epidemic is essentially the same as the number of isolated vertices in a random directed graph. Poisson approximation for the latter quantity is proved using the Stein-Chen method and a suitable coupling.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Deposited On:||13 Apr 2010 14:06|
|Last Modified:||27 Nov 2013 19:20|
|Publisher:||Applied Probability Trust|
|Citations:||Web of Science®. Times Cited: 12|
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