Permanent URL to this publication: http://dx.doi.org/10.5167/uzh22617
Barbour, A D (1994). Threshold phenomena in epidemic theory. In: Kelly, F P. Probability, statistics and optimisation. Chichester: Wiley, 101116.

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Abstract
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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Additional indexing
Item Type:  Book Section, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  510 Mathematics 
Language:  English 
Date:  1994 
Deposited On:  09 Apr 2010 09:25 
Last Modified:  05 Apr 2016 13:27 
Publisher:  Wiley 
Series Name:  Wiley Series in Probability and Mathematical Statistics 
ISBN:  0471948292 
Additional Information:  This is a preprint of an article published in [Barbour, A. D. Threshold phenomena in epidemic theory. Probability, statistics and optimisation, 101116], Wiley Series in Probability and Mathematical Statistics Copyright © 1994 
Related URLs:  http://www.ams.org/mathscinetgetitem?mr=1320745 
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