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

Part of: Markov processes Limit theorems

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

Allen, L. J. S. and Burgin, A. M. (2000). Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math. Biosci. 163, 1–33.Google Scholar
Buckley, F. M. and Pollett, P. K. (2010). Limit theorems for discrete-time metapopulation models. Prob. Surveys 7, 53–83.CrossRefGoogle Scholar
Gani, J., Yakowitz, Y. and Blount, M. (1997). The spread and quarantine of HIV infection in a prison system. SIAM J. Appl. Math. 57, 1510–1530.CrossRefGoogle Scholar
Lekone, P. E. and Finkenstädt, B. F. (2006). Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62, 1170–1177.Google Scholar
McVinish, R. and Pollett, P. K. (2010). Limits of large metapopulations with patch-dependent extinction probabilities. Adv. Appl. Prob. 42, 1172–1186.Google Scholar
Tuckwell, H. C. and Williams, R. J. (2007). Some properties of a simple stochastic epidemic model of SIR type. Math. Biosci. 208, 76–97.Google Scholar