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**Stochastic and deterministic analysis of SIS household epidemics.** / Neal, Peter John.

Research output: Contribution to journal › Journal article › peer-review

Neal, PJ 2006, 'Stochastic and deterministic analysis of SIS household epidemics', *Advances in Applied Probability*, vol. 38, no. 4, pp. 943-968. <http://projecteuclid.org/euclid.aap/1165414587>

Neal, P. J. (2006). Stochastic and deterministic analysis of SIS household epidemics. *Advances in Applied Probability*, *38*(4), 943-968. http://projecteuclid.org/euclid.aap/1165414587

Neal PJ. Stochastic and deterministic analysis of SIS household epidemics. Advances in Applied Probability. 2006 Dec;38(4):943-968.

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title = "Stochastic and deterministic analysis of SIS household epidemics",

abstract = "We analyse SIS epidemics among populations partitioned into households. The analysis considers both the stochastic and deterministic models and, unlike in previous analyses, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R*, is greater than 1. Furthermore, by utilising Markov chains we show that the total number of infectives converges to the endemic equilibrium as t → ∞. For the stochastic model, we prove a law of large numbers result for the convergence, to the deterministic limit, of the mean number of infectives per household. This is followed by the derivation of a Gaussian limit process for the fluctuations of the stochastic model.",

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year = "2006",

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N2 - We analyse SIS epidemics among populations partitioned into households. The analysis considers both the stochastic and deterministic models and, unlike in previous analyses, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R*, is greater than 1. Furthermore, by utilising Markov chains we show that the total number of infectives converges to the endemic equilibrium as t → ∞. For the stochastic model, we prove a law of large numbers result for the convergence, to the deterministic limit, of the mean number of infectives per household. This is followed by the derivation of a Gaussian limit process for the fluctuations of the stochastic model.

AB - We analyse SIS epidemics among populations partitioned into households. The analysis considers both the stochastic and deterministic models and, unlike in previous analyses, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R*, is greater than 1. Furthermore, by utilising Markov chains we show that the total number of infectives converges to the endemic equilibrium as t → ∞. For the stochastic model, we prove a law of large numbers result for the convergence, to the deterministic limit, of the mean number of infectives per household. This is followed by the derivation of a Gaussian limit process for the fluctuations of the stochastic model.

M3 - Journal article

VL - 38

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EP - 968

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

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