In 1868 the accidental introduction into the United States of the cottony cushion insect (Icerya purchasi) from Australia threatened to destroy the American citrus industry.
To counteract this situation, a natural Australian predator, a ladybird beetle (Novius cardinalis) was imported. The beetles kept the scale insects down to a relatively low level. When DDT was discovered to kill scale insects, farmers applied it in the hope of reducing even further the scale insect population. However, DDT turned out to be fatal to the beetle as well, and the overall effect of using the insecticide was to increase the numbers of the scale insect.
Modify the Lotka–Volterra model to reflect a predator–prey system of two insect species where farmers apply (on a continuing basis) an insecticide that destroys both the insect predator and the insect prey at a common rate proportional to the numbers present. What conclusions do you reach concerning the effects of the application of the insecticide? Use graphical analysis to determine the effect of using the insecticide once on an irregular basis.