On the Statistical Measure of Infectiousness

Abstract

WE all recognise that some diseases are more "catching" than others. Every mother knows that measles is very catching and most people set aside a group of common complaints, measles, mumps, whooping-cough, scarlet fever, diphtheria-perhaps roughly in that order-as catching complaints. Then again, still keeping ourselves within the circle of ideas of educated non-medical people, one has such complaints as common colds or influenza which one thinks of as running through a house indeed but does not put quite into the measles category, as one feels that factors determine the spread other than mere proximity to a sick person. Lastly, one has some illnesses, gonorrhoea would be a fair example, which everybody recognises to be spread wholly by contagion, almost always by a particular method of contagion, but does not regard as catching at all in the sense that measles and whooping-cough are catching. When we enquire into the reasons of these opinions they will be found, I think, to be these.An illness is held to be catching when it has usually been possible to explain the existence of a case of it by close association (of some kind) with an immediately pre-existing case; the notion of more or less infectiousness depends upon some appraisement of the proportion of persons attacked to persons exposed to the risk of attack. Mothers observe that when a child sickens with measles most of the other children take the complaint within a period of days or weeks, when a child sickens with scarlet fever the proportion of others attacked is smaller, and so on.When we are dealing practically with such complaints as measles, rough criteria such as these are sufficient; but when we seek a deeper knowledge of the epidemiology even of these common complaints they are inadequate, and when we pass to the debatable region of diseases of which the infectiousness is quite uncertain they are altogether useless. Epidemiologists without any predilections for statistical analysis have, therefore, been forced to give these popular notions an at least quasi-statistical form. They have studied the distribution of "multiple" cases of disease in groups-families, inmates of houses, etc.-and sought to draw conclusions from the frequency distribution. If, they have argued, a "case" does not breed other "cases" in the exposed to risk, then if a number of groups have been observed through a finite interval, we shall find but few instances in which any one group contains more than one affected member, and in those few cases we shall be able to account for the independent origin-independent one of another-of the multiple cases. If, on the other hand, one case does breed others, the more intense the effect the

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