Pheromone trapping models for insect pest control

Summary

Pheromones have recently been suggested for use in insect pest control. We formulate a discrete version of a model with virgin females (or female equivalent of pheromone) in traps, and explore conditions under which this mechanism can eradicate the pest. Our model is density independent, thus when eradication is not possible, the pest increases without bound, in reality density dependent effects limit population growth. Successive refinements incorporating various features, show that delayed mating together with monogamy has a strong influence on the outcome, whereas other aspects of mating behaviour are relatively unimportant. All our models show that when males are in excess control is impossible but when some virgins are left unmated each day the outcome depends on the parameters. As the birth rate or survivorship increase, control by this method becomes more difficult.