On a Statistical Approximation to the Infection Interval

Abstract

IN A PREVIOUS PAPER (2) the existence of strong correlation between the logarithms of the morbidity rates of a group of respiratory diseases for successive calendar month-pairs was demonstrated. The case rates involved pertain to the combined incidence of catarrhal bronchitis, acute coryza, acute catarrhal pharyngitis and laryngitis, and influenza, as diagnosed and reported in the United States Army. Where Ci is the case rate observed in the i-th calendar month, and C, +1 the corresponding rate observed in the succeeding calendar month of the same year (or the same winter when i = December), the value of rlog ci log Ci +. for the twelve month-pairs averaged .84, each of the twelve coefficients being based upon some 38 observations, according to the number of years for which data were available for each month-pair. The purpose of the present paper is to relate some of the results obtained in connection with ref. (2) to the law of mass action in epidemiology, and to derive therefrom an estimate of the infection interval for an assumed period of immunity following infection, or conversely, an estimate of the period of immunity corresponding to a known infection interval. In connection with the actual numerical values presented, it should be noted that they pertain to a group of diseases and therefore can be interpreted only as average for the group as a whole. The law of mass action in epidemiology states that the rate at which a contagious or epidemic disease spreads in a community is proportional to the product of the number of infectious individuals and the number of susceptibles in the community. If two consecutive time intervals are chosen such that the length of each interval is equal to the period between contact and case manifestation (i.e., the incubation period), a contact between an infectious person and a susceptible in the first interval will result in a new case during the second. Then the law of mass action may be written as