麻疹变异性的随机动力学与幂律
Stochastic dynamics and a power law for measles variability.
作者信息
Keeling M, Grenfell B
机构信息
Department of Zoology, University of Cambridge, UK.
出版信息
Philos Trans R Soc Lond B Biol Sci. 1999 Apr 29;354(1384):769-76. doi: 10.1098/rstb.1999.0429.
Abstract
Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size.
摘要
自从发现自然种群的均值和方差之间存在幂律标度关系以来，已在多种物种中观察到这一现象。在此，我们表明，相同形式的幂律标度关系也出现在英格兰和威尔士的麻疹病例报告中。值得注意的是，这种幂律关系在四个数量级上都成立。我们考虑疫苗接种这个自然实验如何影响幂律的斜率。通过研究简单的一般模型，我们能够预测随机性和耦合的影响，并提出一种与临界社区规模相关的新现象。
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本文引用的文献
1
Population dynamic interference among childhood diseases.
Proc Biol Sci. 1998 Nov 7;265(1410):2033-41. doi: 10.1098/rspb.1998.0537.
2
Patterns of density dependence in measles dynamics.
Proc Biol Sci. 1998 May 7;265(1398):753-62. doi: 10.1098/rspb.1998.0357.
3
Empirical determinants of measles metapopulation dynamics in England and Wales.
Proc Biol Sci. 1998 Feb 7;265(1392):211-20. doi: 10.1098/rspb.1998.0284.
4
Persistence, chaos and synchrony in ecology and epidemiology.
Proc Biol Sci. 1998 Jan 7;265(1390):7-10. doi: 10.1098/rspb.1998.0256.
5
Modelling the persistence of measles.
Trends Microbiol. 1997 Dec;5(12):513-8. doi: 10.1016/S0966-842X(97)01147-5.
6
Dynamical complexity in age-structured models of the transmission of the measles virus: epidemiological implications at high levels of vaccine uptake.
Math Biosci. 1996 Dec;138(2):101-30. doi: 10.1016/s0025-5564(96)00127-7.
7
Disease extinction and community size: modeling the persistence of measles.
Science. 1997 Jan 3;275(5296):65-7. doi: 10.1126/science.275.5296.65.
8
Chaos and complexity in measles models: a comparative numerical study.
IMA J Math Appl Med Biol. 1993;10(2):83-95. doi: 10.1093/imammb/10.2.83.
9
An age-structured model of pre- and post-vaccination measles transmission.
IMA J Math Appl Med Biol. 1984;1(2):169-91. doi: 10.1093/imammb/1.2.169.
10
The population dynamics of competition between parasites.
Parasitology. 1985 Oct;91 ( Pt 2):317-47. doi: 10.1017/s0031182000057401.
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