Contribution to the mathematical theory of epidemics
Contribution to the mathematical theory of epidemics
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DOI：
10.1098/rspa.1927.0118
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发表时间：
1927-08-01
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
(1)流行病研究的一个最显著的特点是，很难找到一个因果因素，似乎足以解释几乎所有人口都经常发生的疾病流行的规模。进行这次调查的目的是为了更深入地了解控制传染性流行病传播的各种因素的影响。这里可以参考罗斯和哈德逊（1915- 1917）的著作，他们也讨论了同样的问题。这个问题在这里被带到另一个阶段，从某种意义上说，它是从一个更普遍的观点来考虑的。这个问题可以概括如下：一个（或多个）感染者被引入一个或多或少易感染该疾病的个体社区。这种疾病通过接触感染从患病者传播到未患病者。每一个被感染的人都经历了他的疾病过程，最后通过康复或死亡而从患病的人数中消失。在他患病期间，康复或死亡的可能性每天都在变化。患病者将感染传给未患病者的可能性同样取决于疾病的阶段。随着流行病的蔓延，社区中未受影响的成员人数减少。由于流行病的过程与个人的生命相比是短暂的，人口可以被认为是保持不变的，除非它因流行病本身的死亡而改变。随着时间的推移，这种流行病可能会结束。流行病学中最重要的问题之一是确定这种终止是否仅在没有易感个体时发生，或者感染性、恢复和死亡率等各种因素的相互作用是否可能导致终止，而许多易感个体仍然存在未受影响的人群中。很难从最一般的方面来处理这个问题。在本通讯中，讨论将限于社区所有成员最初对疾病同样易感的情况，并进一步假设完全免疫是由单一感染赋予的。
(1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.