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The SIS Great Circle Epidemic model

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The SIS Great Circle Epidemic model. / Neal, Peter.
In: Journal of Applied Probability, Vol. 45, No. 2, 2008, p. 513-530.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Neal, P 2008, 'The SIS Great Circle Epidemic model', Journal of Applied Probability, vol. 45, no. 2, pp. 513-530. https://doi.org/10.1239/jap/1214950364

APA

Neal, P. (2008). The SIS Great Circle Epidemic model. Journal of Applied Probability, 45(2), 513-530. https://doi.org/10.1239/jap/1214950364

Vancouver

Neal P. The SIS Great Circle Epidemic model. Journal of Applied Probability. 2008;45(2):513-530. doi: 10.1239/jap/1214950364

Author

Neal, Peter. / The SIS Great Circle Epidemic model. In: Journal of Applied Probability. 2008 ; Vol. 45, No. 2. pp. 513-530.

Bibtex

@article{b373de7ec35047978d5e0b82e3c97b1f,
title = "The SIS Great Circle Epidemic model",
abstract = "We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.",
keywords = "SIS epidemic, contact process , great circle model , endemic equilibrium , branching process",
author = "Peter Neal",
year = "2008",
doi = "10.1239/jap/1214950364",
language = "English",
volume = "45",
pages = "513--530",
journal = "Journal of Applied Probability",
publisher = "University of Sheffield",
number = "2",

}

RIS

TY - JOUR

T1 - The SIS Great Circle Epidemic model

AU - Neal, Peter

PY - 2008

Y1 - 2008

N2 - We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.

AB - We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.

KW - SIS epidemic

KW - contact process

KW - great circle model

KW - endemic equilibrium

KW - branching process

U2 - 10.1239/jap/1214950364

DO - 10.1239/jap/1214950364

M3 - Journal article

VL - 45

SP - 513

EP - 530

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 2

ER -