Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22617
Barbour, A D (1994). Threshold phenomena in epidemic theory. In: Kelly, F P. Probability, statistics and optimisation. Chichester, 101-116. ISBN 0-471-94829-2.
The threshold theorem for deterministic epidemics in mixing populations can usually be rewritten in such a form that a large epidemic results from trace infection if and only if $R_0>1$, where $R_0$ can be interpreted as a basic reproduction ratio for an associated population model. The Whittle stochastic threshold theorem replaces certainty with probability: if $R_0\leq 1$, a large epidemic is highly unlikely to result from the introduction of one or two infectives, whereas, if $R_0>1$, the probability of having a significant epidemic is no longer trivial. In this paper, the Whittle approximation to a model for parasitic infection in a mixing population is analysed. A feature of the model is that $R_0$ is well defined, but for certain parameter values the threshold is not at $R_0=1$. Thus to have $R_0=1$ as threshold for epidemics in mixing populations is by no means a universal rule. A related birth and death process with drift is also investigated.
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|Item Type:||Book Section, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Deposited On:||09 Apr 2010 09:25|
|Last Modified:||09 Jul 2012 03:57|
|Series Name:||Wiley Series in Probability and Mathematical Statistics|
|Additional Information:||This is a preprint of an article published in [Barbour, A. D. Threshold phenomena in epidemic theory. Probability, statistics and optimisation, 101--116], Wiley Series in Probability and Mathematical Statistics Copyright © 1994|
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