REPRODUCTION NUMBERS AND THRESHOLDS IN STOCHASTIC EPIDEMIC MODELS .1. HOMOGENEOUS POPULATIONS
REPRODUCTION NUMBERS AND THRESHOLDS IN STOCHASTIC EPIDEMIC MODELS .1. HOMOGENEOUS POPULATIONS
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DOI：
10.1016/0025-5564(91)90003-2
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发表时间：
1991-12-01
影响因子：
4.3
通讯作者：
ONEILL, P
中科院分区：
文献类型：
--
作者：
JACQUEZ, JA;ONEILL, P
我们比较了具有招募、疾病死亡、背景死亡率和传播率β-cXY/N的齐次SI模型的确定性和随机版本的阈值结果。如果一种传染病被引入到一个种群中，基本繁殖数R 0对两者都起着重要的作用，尽管阈值结果略有不同。对于确定性模型，如果R 0小于或等于1，则不会发生流行病，如果R 0> 1，则会发生流行病。对于随机模型，我们发现，平均而言，没有流行病将发生，如果R 0小于或等于1。如果R 0> 1，则存在一个小于1的有限概率，即流行病将发展并最终达到地方病准平衡。然而，也有一个有限的概率灭绝的感染，灭绝的概率下降，随着R 0增加超过1。
We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta-cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the deterministic model, no epidemic can occur if R0 less-than-or-equal-to 1 and an epidemic occurs if R0 > 1. For the stochastic model we find that on average, no epidemic will occur if R0 less-than-or-equal-to 1. If R0 > 1, there is a finite probability, but less than 1, that an epidemic will develop and eventuate in an endemic quasi-equilibrium. However, there is also a finite probability of extinction of the infection, and the probability of extinction decreases as R0 increases above 1.