A set of discrete formulae for the performance of a tsetse population during aerial spraying

Abstract

A set of discrete formulae that calculates the hypothetical impact of aerial spraying on a tsetse population is derived and the work is thought to be novel. Both the original population and the subsequent generations which survive the aerial spraying, may ultimately be thought of as deriving from two, distinct sources. These origins are, however, neither distinct, nor relevant by the third generation. It is for this reason that the female population is considered to be composed of the following four categories for the purposes of derivation: Original flies which existed as such at the commencement of spraying; original pupae which existed as such at the commencement of spraying; the immediate descendants of both the aforementioned categories, during spraying; third and higher generation descendants. In theory, the latter category is a recurrence relation. In practice, the third generation's pupal stage has hardly come into existence, even by the end of a completed operation. Implicit in the formulae is the assumption of one, temperature-dependent mortality rate for the entire pupal stage, a second for the period between eclosion and ovulation and yet a third for the entire, adult life-span. Gravid female resistance to the insecticide is assumed to be inconsequential. A further assumption of the formulae is that at least one male is always available (degree of sterility variable).

An improved temporal formulation of pupal transpiration in Glossina

“…This is since the pupal stage, alone, is neither susceptible to targets, nor aerial spraying. In this regard, it is noteworthy that the eclosion rates in [8] should probably be closer to those in [9], if not higher, for a steady-state equilibrium and the projected outcomes can be adjusted by a very similar factor. The humidities and temperatures referred to in this research have generally been attributed to the pupal substrate, however, one might still wonder whether atmospheric conditions can be wholly ignored.…”

Modelling optimal timing and frequency of insecticide sprays for eradication or knockdown of closed populations of tsetse flies Glossina spp. (Diptera: Glossinidae)

“…Thus, he considered the number of spray cycles required to kill only those adult flies that emerged from pupae deposited prior to the onset of spraying. Later, Childs () considered situations where adults survive spraying, although it was always assumed that the kill rate was ≥ 99%. In a more complete treatment, the present study also considers the fate of pupae produced during the spraying operation by females that survive one or more spraying cycles.…”