A Set of Discrete Formulae for the Performance of a Tsetse Population During Aerial Spraying

TL;DR

This paper derives a set of discrete formulae to estimate the impact of aerial spraying on tsetse fly populations, considering different generational sources and stages, with assumptions on mortality rates and insecticide resistance.

Contribution

It introduces a novel mathematical model that accounts for multiple sources and stages of tsetse populations during aerial spraying.

Findings

Formulae predict population decline post-spraying

Generational analysis shows rapid population reduction

Model incorporates temperature-dependent mortality rates

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).