  An equation, strongly reminiscent of Fisher's equation, is used to model the
response of tsetse populations to proposed control measures in the vicinity of
a game reserve. The model assumes movement is by diffusion and that growth is
logistic. This logistic growth is dependent on an historical population, in
contrast to Fisher's equation which bases it on the present population. The
model therefore takes into account the fact that new additions to the adult fly
population are, in actual fact, the descendents of a population which existed
one puparial duration ago, furthermore, that this puparial duration is
temperature dependent. Artificially imposed mortality is modelled as a
proportion at a constant rate. Fisher's equation is also solved as a formality.
  The temporary imposition of a 2 % $\mathrm{day}^{-1}$ mortality everywhere
outside the reserve for a period of 2 years will have no lasting effect on the
influence of the reserve on either the Glossina austeni or the G. brevipalpis
populations, although it certainly will eradicate tsetse from poor habitat,
outside the reserve. A 5 $\mathrm{km}$-wide barrier with a minimum mortality of
4 % $\mathrm{day}^{-1}$, throughout, will succeed in isolating a worst-case, G.
austeni population and its associated trypanosomiasis from the surrounding
areas. A more optimistic estimate of its mobility suggests a mortality of 2 %
$\mathrm{day}^{-1}$ will suffice. For a given target-related mortality, more
mobile species are found to be more vulnerable to eradication than more
sedentary species, while the opposite is true for containment.
