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The great circle epidemic model

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The great circle epidemic model. / Ball, Frank; Neal, Peter John.
In: Stochastic Processes and their Applications, Vol. 107, No. 2, 2003, p. 233-268.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Ball, F & Neal, PJ 2003, 'The great circle epidemic model', Stochastic Processes and their Applications, vol. 107, no. 2, pp. 233-268. https://doi.org/10.1016/S0304-4149(03)00074-7

APA

Ball, F., & Neal, P. J. (2003). The great circle epidemic model. Stochastic Processes and their Applications, 107(2), 233-268. https://doi.org/10.1016/S0304-4149(03)00074-7

Vancouver

Ball F, Neal PJ. The great circle epidemic model. Stochastic Processes and their Applications. 2003;107(2):233-268. doi: 10.1016/S0304-4149(03)00074-7

Author

Ball, Frank ; Neal, Peter John. / The great circle epidemic model. In: Stochastic Processes and their Applications. 2003 ; Vol. 107, No. 2. pp. 233-268.

Bibtex

@article{d4a15f41708a4c9c8e4aaf33f7186140,
title = "The great circle epidemic model",
abstract = "We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n→∞ is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n→∞ by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution",
keywords = "Branching process, Central limit theorems, Coupling, Epidemic process, Small-world models, Weak convergence",
author = "Frank Ball and Neal, {Peter John}",
year = "2003",
doi = "10.1016/S0304-4149(03)00074-7",
language = "English",
volume = "107",
pages = "233--268",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - The great circle epidemic model

AU - Ball, Frank

AU - Neal, Peter John

PY - 2003

Y1 - 2003

N2 - We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n→∞ is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n→∞ by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution

AB - We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n→∞ is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n→∞ by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution

KW - Branching process

KW - Central limit theorems

KW - Coupling

KW - Epidemic process

KW - Small-world models

KW - Weak convergence

U2 - 10.1016/S0304-4149(03)00074-7

DO - 10.1016/S0304-4149(03)00074-7

M3 - Journal article

VL - 107

SP - 233

EP - 268

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 2

ER -