Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

On a reaction-diffusion model for sterile insect release method with release on the boundary
Pages: 2509 - 2522, Issue 7, October 2012

doi:10.3934/dcdsb.2012.17.2509      Abstract        References        Full text (254.4K)           Related Articles

Xin Li - Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China (email)
Xingfu Zou - Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada (email)

1 H. J. Barclay, The sterile release method for population control with interspecific competition, Res. Pop. Ecol., 23 (1981), 145-155.
2 H. J. Barclay, Models for pest control: Complementary effects of periodic release of sterile pests and parasitoids, Theor. Pop. Biol., 32 (1987), 76-89.
3 H. J. Barclay, Demographic consequences of monogamy and polygamy for a sterile release program, Protection Ecol., 6 (1984), 209-217.
4 H. J. Barclay and M. Mackauer, The sterile insect release method for pest control: A density dependent model, Envir. Entom., 9 (1980), 810-817.
5 H. J. Barclay and M. Mackauer, Effects of sterile insect releases on a population under predation or parasitism, Res. Pop. Ecol., 22 (1980), 136-146.
6 A. H. Baumhover, A. J. Graham, B. A. Bitter, D. E. Hopkins, W. D. New, F. H. Dudley and R. C. Bushland, Screwworm control though release of sterilized flies, J. Econ. Entomol., 48 (1955), 462-466.
7 A. A. Berryman, Mathematical description of the sterile male principle, Can. Entomol., 99 (1967), 858-865.
8 K. Dietz, The effect of immigration on genetic control, Theor. Popul. Biol., 9 (1976), 58-67.
9 Y. H. Du, "Order Structure and Topological Methods in Nonlinear PDEs. Vol. 1. Maximum Principle and Applications,'' World Scientific, Singapore, 2005.
10 H. M. Graham, Sterile pink bollworm: Field release for population suppression, J. Econ. Entomol., 71 (1978), 233-235.
11 G. W. Harrison, H. J. Barclay and P. van den Driessche, Analysis of a sterile release model with predation, J. Math. Biol., 16 (1982/83), 33-48.       
12 Y. Ito, A model of sterile insect release for eradication of the melon fly, Dacus cucurbitae COQUILLETT. Appl. Ent. Zool., 12 (1977), 303-310.
13 O. Iwahashi, Eradication of the melon fly, Dacus eucurbitae, from Kume Is. Okinawa. with the sterile insect release method, Res. Popul. Ecol., 19 (1977), 87-98.
14 W. Jiang, X. Li and X. Zou, On a reaction-diffusion model for sterile insect release method in a bounded domain, submitted.
15 E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males, J. Econ. Entomol., 48 (1955), 459-462.
16 E. S. Krafsur, H. Townson, G. Davidson and C. F. Curtis, Srewworm eradication is what it seems, Nature, 323 (1986), 495-496.
17 M. A. Lewis and P. van Den Driessche, Waves of extinction from sterile insect release, Math. Biosci., 5 (1992), 221-247.
18 A. W. Lindquist, The use of gamma radiation for control or eradication of the Screw-worm, J. Econ. Entomol., 48 (1955), 467-469.
19 V. S. Manoranjan and P. van den Driessche, On a diffusion model for sterile insect release, Math. Biosci., 79 (1986), 199-208.       
20 D. R. Miller and D. E. Weidhaas, Equilibrium populations during a sterile release program, Environ. Entomol., 3 (1974), 211-216.
21 C. V. Pao, "Nonlinear Parabolic and Elliptic Equations,'' Plenum Press, New York, 1992.       
22 R. E. Plant and R. T. Cunningham, Analysis of the dispersal of sterile Mediterranean fruit flies (Diptera: Tephritidae) released from a point source, Environ. Entomol., 20 (1991), 1493-1530.
23 R. E. Plant and M. Mangel, Modeling and simulation in agricultural pest management, SIAM Rev., 29 (1987), 235-261.       
24 T. Prout, The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population, Theor. Popul. Biol., 13 (1978), 40-71.
25 M. D. Proverbs, J. R. Newton and D. M. Logan, Codling moth control by the sterility method in twenty-one British Columbia orchards, J. Econ. Entomol., 70 (1977), 667-671.
26 H. L. Smith, "Monotone Dynamical System: An introduction to the Theory of Competitive and Cooperative Systems,'' Mathematical Surveys and Monographs, 41, AMS, Providence, RI, 1995.       

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