Let x(t) be a harmful insect population (aphids) that

Chapter 7, Problem 7.4.3

(choose chapter or problem)

Let x(t) be a harmful insect population (aphids?) that under natural conditions is held somewhat in check by a benign predator insect population y(t) (ladybugs?). Assume that x(t) and y(t) satisfy the predator-prey equations in (1), so that the stable equilibrium populations are xE = b/q and YE = a/po Now suppose that an insecticide is employed that kills (per unit time) the same fraction f < a of each species of insect. Show that the harmful population xE is increased, while the benign population YE is decreased, so the use of the insecticide is counterproductive. This is an instance in which mathematical analysis reveals undesirable consequences of a well-intentioned interference with nature.