title: Analysis of sustainable pest control using a pesticide and a screened refuge.
abstract: We describe and analyze a 'screened refuge' technique for indefinitely sustaining control of insect pests using transgenic pesticidal crops or an applied pesticide, even when resistance is not recessive. The screen is a physical barrier that restricts pest movement. In a deterministic discrete-time model of the use of this technique, we obtain asymptotic analytical formulas for the two important equilibria of the system in terms of the refuge size and the pest fitnesses, mutation rates, and mobility out of and into the refuge. One of the equilibria is stable and is the point at which the pest population is controlled. The other is a saddle whose stable manifold bounds the basin of attraction of the former: its location provides a measure of the tolerance of the control mechanism to perturbations in the resistant allele density.
authors.affiliation: Department of Mathematics, University at Buffalo Buffalo, NY, USA.
authors.forename: John
authors.initials: J
authors.lastname: Ringland
authors.affiliation: Department of Mathematics, University of Rhode Island Kingston, RI, USA.
authors.forename: Prasanth
authors.initials: P
authors.lastname: George
keywords: caged refuge; insecticidal crops; non-recessive resistance; pest control; population genetics; refuge; resistance evolution; screened refuge; sustainable; transgenic