We derive a simple but surprising connection between the ''determinist
ic epidemic with recovery'' and the spatial birth-and-death process, a
nd discuss its implications for the use of nonlinear differential equa
tion models for the spatial spread of epidemics. This paper consists o
f a manuscript dating back to 1977, which has been widely referred to
in the literature but not previously published, and its more recent ex
tension to include recovery/death in the processes considered, with so
me additional comments. To aid reference, we retain the original title
.