Department of Mathematics and Applied Mathematics, University of the Free State, South Africa.
Acta Trop. 2013 Feb;125(2):202-13. doi: 10.1016/j.actatropica.2012.08.015. Epub 2012 Sep 11.
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).
一组离散公式，用于计算空中喷洒对采采蝇种群的假设影响，这项工作被认为是新颖的。最初的种群和随后在喷洒中幸存下来的后代，最终可能被认为是来自两个不同的来源。然而，到了第三代，这些来源既不明显，也不相关。出于这个原因，为了推导的目的，雌性种群被认为由以下四个类别组成：在喷洒开始时就存在的原始成虫；在喷洒开始时就存在的原始蛹；在喷洒期间上述两个类别的直接后代；第三代及更高代的后代。从理论上讲，后一类是递归关系。实际上，即使在一个完整的操作结束时，第三代的蛹期也几乎没有出现。公式中隐含着一个假设，即整个蛹期有一个温度相关的死亡率，从羽化到排卵期间有第二个死亡率，整个成虫寿命期间有第三个死亡率。假设雌性对杀虫剂的抗药性微不足道。公式的另一个假设是，始终至少有一只雄性可用（绝育程度可变）。
