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A Central Limit Theorem for a Discrete-Time SIS Model with Individual Variation

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  04 February 2016

R. McVinish  and
P. K. Pollett
R. McVinish*
Affiliation:
University of Queensland
P. K. Pollett*
Affiliation:
University of Queensland
*
∗ Postal address: School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia.
∗ Postal address: School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia.
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Abstract

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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.

Keywords

Epidemic modellingfixed pointmetapopulation modellingweak convergence

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 521 - 530
Copyright
© Applied Probability Trust 

References

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