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The probability of extinction of a dynamic epidemic model

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The probability of extinction of a dynamic epidemic model. / Neal, Peter John.
In: Mathematical Biosciences, Vol. 236, No. 1, 03.2012, p. 31-35.

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

Harvard

Neal, PJ 2012, 'The probability of extinction of a dynamic epidemic model', Mathematical Biosciences, vol. 236, no. 1, pp. 31-35. https://doi.org/10.1016/j.mbs.2012.01.002

APA

Neal, P. J. (2012). The probability of extinction of a dynamic epidemic model. Mathematical Biosciences, 236(1), 31-35. https://doi.org/10.1016/j.mbs.2012.01.002

Vancouver

Neal PJ. The probability of extinction of a dynamic epidemic model. Mathematical Biosciences. 2012 Mar;236(1):31-35. doi: 10.1016/j.mbs.2012.01.002

Author

Neal, Peter John. / The probability of extinction of a dynamic epidemic model. In: Mathematical Biosciences. 2012 ; Vol. 236, No. 1. pp. 31-35.

Bibtex

@article{f6c0fea2c1974375946c877d37e3951d,
title = "The probability of extinction of a dynamic epidemic model",
abstract = "We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R0, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N → ∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R0 and the probability of extinction. However, it is shown that for n = 2, the basic reproduction number, R0, is maximised by a constant length infectious period and is decreasing in ς, the speed of movement between the two populations.",
keywords = "Dynamic SIR epidemics, Branching process approximation, Extinction probability, Basic reproduction number",
author = "Neal, {Peter John}",
year = "2012",
month = mar,
doi = "10.1016/j.mbs.2012.01.002",
language = "English",
volume = "236",
pages = "31--35",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - The probability of extinction of a dynamic epidemic model

AU - Neal, Peter John

PY - 2012/3

Y1 - 2012/3

N2 - We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R0, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N → ∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R0 and the probability of extinction. However, it is shown that for n = 2, the basic reproduction number, R0, is maximised by a constant length infectious period and is decreasing in ς, the speed of movement between the two populations.

AB - We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R0, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N → ∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R0 and the probability of extinction. However, it is shown that for n = 2, the basic reproduction number, R0, is maximised by a constant length infectious period and is decreasing in ς, the speed of movement between the two populations.

KW - Dynamic SIR epidemics

KW - Branching process approximation

KW - Extinction probability

KW - Basic reproduction number

U2 - 10.1016/j.mbs.2012.01.002

DO - 10.1016/j.mbs.2012.01.002

M3 - Journal article

VL - 236

SP - 31

EP - 35

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -