Contributions to the mathematical theory of epidemics II - The problem of endemicity
Contributions to the mathematical theory of epidemics II - The problem of endemicity
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DOI：
10.1098/rspa.1932.0171
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发表时间：
1932-10-01
期刊：
影响因子：
--
通讯作者：
McKendrick, AG
中科院分区：
文献类型：
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作者：
Kermack, WO;McKendrick, AG
在前一次通讯中，曾试图用数学方法研究在封闭的易感人群中流行的过程。为了简化问题，提出了一些明确的假设，即所有人都同样容易受到影响，袭击造成死亡或完全豁免。个体的传染性及其死亡或康复的机会由任意函数表示，并且假定发生新感染的机会与人口中受感染和易受感染成员的乘积成正比。尽管引入了任意函数，但结果表明，总体上存在一个临界人口密度，如果实际人口密度小于此，则不会发生流行病，但如果超过此密度，则在引入感染焦点时出现流行病，并且如果相对于人口密度较小，则流行病的规模为每单位面积2个。结果表明，这些结论可以很容易地推广到转原性疾病的情况，即通过中间宿主传播的疾病。本文的目的是考虑在种群中不断引入新的易感个体的影响。似乎有必要对这一点进行调查，因为这可能不仅可以解释人类社区中疾病发病率的某些方面，在这些社区中通常有新的易感个体通过移民或出生涌入，而且在托普利和其他人所做的动物实验中也是如此，他们以恒定的速度将新鲜的动物引入已经出现疾病的笼子中，从中获得某些明确的结果。
In a previous communication an attempt was made to investigate mathematically the course of an epidemic in a closed population of susceptible individuals. In order to simplify the problem certain definite assumptions were made, namely, that all individuals were equally susceptible, and that death resulted, or complete immunity was conferred, as the result of an attack. The infectivity of the individual and his chances of death or recovery were represented by arbitrary functions, and the chance of a new infection occurring was assumed to be proportional to the product of the infected and susceptible members of the population. In spite of the introduction of the arbitrary functions, it was shown that in general a critical density of population existed, such that if the actual density was less than this, no epidemic could occur, but if it exceeded this bynan epidemic would appear on the introduction of a focus of infection, and further that ifnwas small relative to the population density, the size of the epidemic would be 2nper unit area. It was shown that these conclusions could be readily extended to the case of a metaxenous disease, that is, one in which transmission takes place through an intermediate host. It is the purpose of the present paper to consider the effect of the continuous introduction of fresh susceptible individuals into the population. It appeared desirable to investigate this point, since it might make it possible to interpret certain aspects of the incidence of disease not only in human communities where there is usually an influx of fresh susceptible individuals either by immigration or by birth, but also in the animal experiments carried out by Topley and others—where fresh animals were introduced at a constant rate into the cages in which cases of disease were already present—from which certain definite results were obtained.