Theory and Observation in Family Epidemics of the Common Cold

Recent developments in the mathematical theories of chance behaviour have quickened interest in their applications to epidemic experience. Theoretical epi demiology aims at the prediction of the likely flow of infection within a group given certain assumptions about the laws underlying epidemic events. Ross (1915), for example, deduced the rise and fall of malarial incidence which would derive from some basic axioms about the frequency of infective mos quitos biting susceptible hosts during their period of contact; Macdonald (1953) has brought this approach up to date by comparing field observations of malarial epidemics with expectation based on a mathematical model of the likely pattern of events. The practical importance of such work lies in the possibility of distinguishing those theories of epi demic behaviour which best fit the observed facts, in the hope that this will lead to a clearer understanding of the factors which determine that behaviour. Most of the work in the field has dealt with major epidemics in large populations using "deterministic" models, i.e. when the future course of the epidemic is precisely determined by basic assumptions about the numbers of susceptibles and the frequency and intimacy of their contact with an infective source. In smaller groups, the likelihood of one susceptible making effective contact with an infectious member of the same group cannot be exactly predicted, for the element of chance bulks larger as the size of the group decreases. In these circumstances, this chance element has to be more carefully taken into account, and here the newer theories of stochastic behaviour have proved useful. Bailey (1957) gives a scholarly review of this development. It is enough to say that Greenwood (1931) introduced the idea that the spread of measles within a household could be described in terms of a series or chain of chance events which followed the usual binomial expression of the law of probability. Any one of three susceptible