Biology – Quantitative Biology – Quantitative Methods
Scientific paper
2009-10-15
Biology
Quantitative Biology
Quantitative Methods
Scientific paper
An equation, strongly reminiscent of Fisher's equation, is used to model the response of tsetse populations to proposed control measures in the vicinity of a game reserve. The model assumes movement is by diffusion and that growth is logistic. This logistic growth is dependent on an historical population, in contrast to Fisher's equation which bases it on the present population. The model therefore takes into account the fact that new additions to the adult fly population, are in actual fact, the descendents of a population which existed one puparial duration ago, furthermore, that this puparial duration is temperature dependent. Artificially imposed mortality is modelled as a straight-forward linear rate. Fisher's equation is also solved as a formality. The temporary imposition of a 2 %/day mortality everywhere outside the reserve for a period of 2 years will have no lasting effect on the influence of the reserve on either the Glossina austeni or the G. brevipalpis population, although it certainly will eradicate tsetse from poor habitat, outside the reserve. A 5 km-wide barrier with a minimum mortality of 4 %/day throughout, will succeed in completely isolating a worst-case, G. austeni population and its associated trypanosomiasis from the surrounding areas. A more optimistic estimate of its mobility suggests a mortality of 2 %/day might suffice. For a given mortality, more mobile species are found to be more vulnerable to eradication than more sedentary species, while the opposite is true for containment.
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