H.S. Wilf and M. Golubitsky

A Computer Simulation in the Study of the Communicability of Diseases

Report, Department of Mathematics, University of Pennsylvania. (1966)

In the period 1957-1960 in Niles, illinois, 11 cases of leukemia were observed. The population of Niles (20,393) was such that about two or three cases should have been expected in such a period. Evidently, in this situation the question of paramount importance is to decide whether or not such an event can be explained on purely random grounds, or else whether some mechanism of communicability or common etiology is operating.

We ask: What is the probability that if statistics on leukemia are accumulated for say 25 years, that is some 2.5 year period in some city the size of Niles, 11 cases will be observed. We use Monte Carlo simulation to distribute the cases randomly around the United States and find that the probability of 11 cases is approximately 0.96. We also observe that the probability of 12 cases is approximately 0.36.