  Many cell populations, exemplified by certain tumors, grow approximately
according to a Gompertzian growth model which has a slower approach to an upper
limit than that of logistic growth. Certain populations of animals and other
organisms have also recently been analyzed with the Gompertz model. This
article addresses the question of how long it takes to reduce the population
from one level to a lower one under a schedule of sudden decrements, each of
which removes a given fraction of the cell mass or population. A deterministic
periodic schedule is first examined and yields exact results for the
eradication or extinction time which is defined as that required to reduce the
number of cells to less than unity. The decrements in cell mass at each hit
could correspond to an approximation to reduction of a tumor by external beam
radiation therapy. The effects of variations in magnitude of successive
decrements, the time interval between them, the initial population size and the
intrinsic growth rate are calculated and results presented graphically.
  With a schedule governed by a Poisson process, the number of organisms or
cells satisfies a stochastic differential equation whose solution sample paths
have downward jumps as random times. The moments of the exit time then satisfy
a system of recurrent differential-difference equations. A simple
transformation results in a simpler system which has been studied both
analytically and numerically in the context of interspike intervals of a model
neuron. Results are presented for the mean eradication time for various
frequencies and magnitudes of hits and for various eventual and initial
population sizes. The standard deviation of the eradication time is also
investigated.
