Contributions to the mathematical theory of epidemics. III.—Further studies of the problem of endemicity

Abstract

In a previous paper (Part II of this series) an attempt was made to treat from a general point of view the problem of a single disease in a population which consisted of three categories of people—namely, never infected, sick and recovered—and in which the infectivity of the disease was a function of the period of illness, whilst the susceptibility of a recovered person was a function of the period which had elapsed since the time of his recovery. New individuals entering the population either by birth or by immigration naturally entered the category of the never infected which for convenience we called “virgins.” It was pointed out that the results obtained were subject to two important limitations: (1) that the disease under consideration was the only cause of death, and (2) that the age of the individuals did not affect their infectivity, susceptibility or reproductiveness. It is the purpose of the present paper to remove the first of these limitations by the introduction of constant non-specific death rates, which for the sake of generality are assumed to be different for virgins, sick, and recovered. It may be stated at once that the introduction of this additional factor produces surprisingly little change in the general nature of the results previously obtained, and that the conclusions of the previous paper hold with very little modifica­tion.