XIV.—The Mathematical Theory of Random Migration and Epidemic Distribution

Abstract

The general theory of epidemic disease I have already considered in a communication to this Society. In that communication I showed that the course of epidemics of all forms of infectious disease obeyed certain very definite laws. In the same paper it was also shown that the distribution of epidemic disease in a uniformly populated area obeyed a law essentially similar. Certain reasons were given why the normal curve of errormight be expected to give an approximate solution in both the cases considered, but why the distribution actually found (type iv.) should be the common form was not at all clear. I think, however, I have now arrived at the solution.

Effect of spatially restricted pollen flow on spatial genetic structure of an animal-pollinated allogamous plant population

“…We assumed that pollen flow follows a negative exponential formula which was first presented by Brownlee(1911):…”

Spread of invading organisms

“…Apart from some early work on epidemics (Brownlee 1911), the first mathematical descriptions of spread originated with population geneticists (Fisher 1937;Kolmogorov et al 1937;Wright 1943, 1947). In the ecological literature, the major early contributions were Skellam (1951) and Kierstead and Slobodkin (1953).…”

Distance Transformation and Distance Decay Functions

“…However, perhaps a more important indication is the paper by the French geneticist J.-M. Goux Special cases that occur in the single-log case are (1) the exponential model [4,9] when m = 1:…”