Abstract
This is a doctoral thesis in the control of pests and diseases. The type of pest of concern to us will lead a life cycle with distinct developmental stages, specifically juvenile and adult. We will construct adult-stage impulsive culling regimes to eradicate a population of such a pest as well as discover that poorly planned regimes may, perversely, benefit the pest. Real-world applications will include the control of insects that act as crop pests or that act as vectors in the spread of human or livestock diseases. Our disease control work will focus on three problems, essentially unrelated except in so far as each has been little explored until now. In the first of these problems, we investigate an SIR model with growing total population and a contact rate that grows with the population; in the second we seek successful pulse vaccination strategies in a metapopulation SIR model; and in the third we derive and study an SIR model with a gestation delay. Suggestions for future research are given at the end.