  The hypothetical impact of aerial spraying on tsetse fly populations is
investigated. Spray cycles are scheduled at intervals two days short of the
first interlarval period and halted once the last of the female flies that
originated from pre-spray-deposited pupae have been sprayed twice. The effect
of temperature on the aerial spraying of tsetse, through its reproductive cycle
and general population dynamics, is of particular interest, given that cooler
weather is preferred for the settling of insecticidal droplets. Spray efficacy
is found to come at a price due to the greater number of cycles necessitated by
cooler weather. The extra cost is argued to be worth while. Pupae, still in the
ground at the end of spraying, are identified as the main threat to a
successful operation. They are slightly more vulnerable at the low temperature
extreme of tsetse habitat (16 $^\circ$C), when the cumulative, natural pupal
mortality is high. One can otherwise base one's expectations on the closeness
with which the time to the third last spray approaches one puparial duration. A
disparity of anything close to the length of a spray cycle advocates caution,
whereas one which comes close to vanishing should be interpreted as being
auspicious. Three such key temperatures, just below which one can anticipate an
improved outcome and just above which caution should be exercised, are 17.146
$^\circ$C, 19.278 $^\circ$C and 23.645 $^\circ$C. A refinement of the existing
formulae for the puparial duration and the first interlarval period might be
prudent in the South African context of a sympatric Glossina brevipalpis-G.
austeni, tsetse population. The resulting aerial spraying strategy would then
be formulated using a G. brevipalpis puparial duration and a G. austeni first
interlarval period.
