Journal of Applied Probability

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

R. McVinish and P. K. Pollett

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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.

Article information

J. Appl. Probab., Volume 49, Number 2 (2012), 521-530.

First available in Project Euclid: 16 June 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Epidemic modelling fixed point metapopulation modelling weak convergence


McVinish, R.; Pollett, P. K. A central limit theorem for a discrete-time SIS model with individual variation. J. Appl. Probab. 49 (2012), no. 2, 521--530. doi:10.1239/jap/1339878802.

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