A central limit theorem for a discrete-time SIS model with individual variation

McVinish, R. and Pollett, P.K. (2012) A central limit theorem for a discrete-time SIS model with individual variation. Journal of Applied Probability, 49 2: 521-530.


Author McVinish, R.
Pollett, P.K.
Title A central limit theorem for a discrete-time SIS model with individual variation
Journal name Journal of Applied Probability   Check publisher's open access policy
ISSN 0021-9002
1475-6072
Publication date 2012-06
Sub-type Article (original research)
DOI 10.1239/jap/1339878802
Volume 49
Issue 2
Start page 521
End page 530
Total pages 10
Place of publication Sheffield, United Kingdom
Publisher Applied Probability Trust
Collection year 2013
Language eng
Abstract A discrete-time SIS model is presented that allows individuals in the population to vary in terms of their susceptibility to infection and their rate of recovery. This model is a generalisation of the metapopulation model presented in McVinish and Pollett (2010). The main result of the paper is a central limit theorem showing that fluctuations in the proportion of infected individuals around the limiting proportion converges to a Gaussian random variable when appropriately rescaled. In contrast to the case where there is no variation amongst individuals, the limiting Gaussian distribution has a nonzero mean.
Keyword Epidemic modelling
Fixed point
Metapopulation modelling
Weak convergence
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
 
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Created: Mon, 18 Jun 2012, 08:16:53 EST by Dr Ross Mcvinish on behalf of Mathematics