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Many cell populations, exemplified by certain tumors, grow approximatelyaccording to a Gompertzian growth model which has a slower approach to an upperlimit than that of logistic growth. Certain populations of animals and otherorganisms have also recently been analyzed with the Gompertz model. Thisarticle addresses the question of how long it takes to reduce the populationfrom one level to a lower one under a schedule of sudden decrements, each ofwhich removes a given fraction of the cell mass or population. A deterministicperiodic schedule is first examined and yields exact results for theeradication or extinction time which is defined as that required to reduce thenumber of cells to less than unity. The decrements in cell mass at each hitcould correspond to an approximation to reduction of a tumor by external beamradiation therapy. The effects of variations in magnitude of successivedecrements, the time interval between them, the initial population size and theintrinsic growth rate are calculated and results presented graphically.  With a schedule governed by a Poisson process, the number of organisms orcells satisfies a stochastic differential equation whose solution sample pathshave downward jumps as random times. The moments of the exit time then satisfya system of recurrent differential-difference equations. A simpletransformation results in a simpler system which has been studied bothanalytically and numerically in the context of interspike intervals of a modelneuron. Results are presented for the mean eradication time for variousfrequencies and magnitudes of hits and for various eventual and initialpopulation sizes. The standard deviation of the eradication time is alsoinvestigated.

Gompertzian population growth under some deterministic and stochastic jump schedules