In 1954, Armitage and Doll published one of the most influential papers in the history of mathematical epidemiology. However, when one examines the literature one finds that there are in fact at least three distinct mathematical models attributed to the 1954 paper. In this study, we examine this important paper and the mathematical derivation of their model. We find, very surprisingly, that no stochastic process can account for all the assumptions of the model and that many of the models in the literature use a consistent subset of the assumptions used in Armitage and Doll's paper.
Billings, W. Zane; Clifton, Justin; Hiller, Josh; Meek, Tommy; Penland, Andrew; Rogers, Wesley; Smokovich, Gabriella; Velasquez-Berroteran, Andrew; and Zamagias, Eleni
"An Axiomatic and Contextual Review of the Armitage and Doll Model of Carcinogenesis,"
Spora: A Journal of Biomathematics: Vol. 8, 7–15.
Available at: https://ir.library.illinoisstate.edu/spora/vol8/iss1/3