Theoretical levels of control as a function of mean temperature and spray efficacy in the aerial spraying of tsetse fly

▶ Pupae, still in the ground at the end of spraying, are identified as the main threat to successful control by aerial spraying. They are, far-and-away, predominantly the immediate descendants of pre-spray-deposited pupae, which ecloded during spraying. ▶ The constant-temperature formula for flies ecloding from such female pupae, ηγ2Nβ∑t⌣=σ(s−1)+1σ(s−1)+τ0∑i=0floort⌣−τ0−τ1−1/τ2e−δ(τ0+τ1+iτ2,T)ϕ(floor{(t⌣−τ0)/σ}−floor{(t⌣−τ0−τ1−iτ2)/σ})[1−H(t⌣−2τ0−τ1−iτ2)]H(t⌣−τ0−τ1), is a good approximation of the outcome of a spraying operation, given the kind of kill rates which can be expected. ▶ One can base one's expectations on the closeness with which the time to the third-last spray cycle approaches one puparial duration. ▶ Three such key temperatures, just below which one can anticipate an improved outcome and just above which caution should be exercised, are 17.146 °C, 19.278 °C and 23.645 °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.