Contributions to the mathematical theory of epidemics: V. Analysis of experimental epidemics of mouse-typhoid; a bacterial disease conferring incomplete immunity

Abstract

In a recently published paper (Kermack & McKendrick, 1937) the observational data relating to epidemics of ectromelia in populations of mice maintained under experimental conditions (Greenwood et al. 1936) has been analysed in the light of a mathematical theory of epidemics developed by us during recent years (Kermack & McKendrick, 1927, 1932, 1933, 1936). It was shown that the life table giving the chance of mice surviving for various lengths of time in infected communities is very closely represented by a formula calculated on the assumption that the various rates—infection rate, recovery rate, death rate, etc.—are constants. It is, of course, realized that this simplifying assumption can only be regarded as approximately true. It renders the application of the general theory practicable, and the result of the investigation justifies its use, in so far as the theory so simplified does actually conform to the experimental results.