The Detection of Space-Time Interactions

THE nature of epidemics has often been approached through the construction of mathematical models and comparison between them and the patterns of observed events. Not infrequently the models have proved easier to construct than the observations have been to assemble. A situation has resulted analogous to that in the field of virology, where a list of viruses with no known diseases, the 'orphan viruses', is currently accumulating while a number of diseases evidently infective in nature persistently refuse to yield their organisms. So it is also in epidemiology. On the one hand we have a series of elegant mathematical solutions to non-existent problems and on the other hand serious difficulty in deciding whether or not many diseases can be regarded as having epidemic or contagious characteristics. It is with the latter aspect that I wish to deal. Basically the question reduces to arriving at a definition of epidemicity and this turns out to be difficult. Most definitions reduce the concept to one of excessive (i.e. non-random) variability of incidence or prevalence and in so doing at least succeed in resolving the problem into two parts. First, prevalence and incidence are large number concepts and are customarily thought of as continuously variable quantities. True, the random element in their variability is recognised as a function of the number of events in a chosen unit of time and if an epidemic is plotted on a time chart the events are added discretely as spots, squares or other symbols, but in pictorial terms it is the heights of the columns which serve to guide the eye and to indicate an epidemic. An epidemic wave here is a movement transverse to the time axis. However, when events are so widely scattered that most of the time units are empty and two events seldom or never occur in the same time unit, the concept of an epidemic in these terms begins to break down. It may be possible to group time units together to restore the customary picture but this is not always a simple and arbitrary matter of presentation. If the events are sparse in relation to the 'wave-length' of the epidemic pattern we have no option but to consider epidemicity not in terms of prevalence but in terms of the lengths of the intervals between discrete events. Any useful concept of epidemicity at this level is a corpuscular one and the methodological problems in many respects analogous with those of the physicist studying low-intensity radiation. The second part of the problem arising from the customary definition of epidemicity is what to do with the geographical element of an