-
Previous Article
Interface oscillations in reaction-diffusion systems above the Hopf bifurcation
- DCDS-B Home
- This Issue
-
Next Article
Dynamics of a 2D Stochastic non-Newtonian fluid driven by fractional Brownian motion
On a reaction-diffusion model for sterile insect release method with release on the boundary
1. | Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China |
2. | Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 |
References:
[1] |
H. J. Barclay, The sterile release method for population control with interspecific competition, Res. Pop. Ecol., 23 (1981), 145-155.
doi: 10.1007/BF02514097. |
[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.
doi: 10.1016/0040-5809(87)90041-4. |
[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.
doi: 10.1007/BF02513541. |
[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.
doi: 10.4039/Ent99858-8. |
[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 (): 33.
doi: 10.1007/BF00275159. |
[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. |
show all references
References:
[1] |
H. J. Barclay, The sterile release method for population control with interspecific competition, Res. Pop. Ecol., 23 (1981), 145-155.
doi: 10.1007/BF02514097. |
[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.
doi: 10.1016/0040-5809(87)90041-4. |
[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.
doi: 10.1007/BF02513541. |
[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.
doi: 10.4039/Ent99858-8. |
[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 (): 33.
doi: 10.1007/BF00275159. |
[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. |
[1] |
Luis F. Gordillo. Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population. Mathematical Biosciences & Engineering, 2014, 11 (3) : 511-521. doi: 10.3934/mbe.2014.11.511 |
[2] |
Chiara Corsato, Franco Obersnel, Pierpaolo Omari, Sabrina Rivetti. On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space. Conference Publications, 2013, 2013 (special) : 159-169. doi: 10.3934/proc.2013.2013.159 |
[3] |
Meng Fan, Bingbing Zhang, Michael Yi Li. Mechanisms for stable coexistence in an insect community. Mathematical Biosciences & Engineering, 2010, 7 (3) : 603-622. doi: 10.3934/mbe.2010.7.603 |
[4] |
Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei. The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Discrete and Continuous Dynamical Systems - B, 2014, 19 (5) : 1373-1410. doi: 10.3934/dcdsb.2014.19.1373 |
[5] |
Junping Shi, Jimin Zhang, Xiaoyan Zhang. Stability and asymptotic profile of steady state solutions to a reaction-diffusion pelagic-benthic algae growth model. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2325-2347. doi: 10.3934/cpaa.2019105 |
[6] |
Arti Mishra, Benjamin Ambrosio, Sunita Gakkhar, M. A. Aziz-Alaoui. A network model for control of dengue epidemic using sterile insect technique. Mathematical Biosciences & Engineering, 2018, 15 (2) : 441-460. doi: 10.3934/mbe.2018020 |
[7] |
Shin-Yi Lee, Shin-Hwa Wang, Chiou-Ping Ye. Explicit necessary and sufficient conditions for the existence of a dead core solution of a p-laplacian steady-state reaction-diffusion problem. Conference Publications, 2005, 2005 (Special) : 587-596. doi: 10.3934/proc.2005.2005.587 |
[8] |
Thomas Lepoutre, Salomé Martínez. Steady state analysis for a relaxed cross diffusion model. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 613-633. doi: 10.3934/dcds.2014.34.613 |
[9] |
Jing Liu, Xiaodong Liu, Sining Zheng, Yanping Lin. Positive steady state of a food chain system with diffusion. Conference Publications, 2007, 2007 (Special) : 667-676. doi: 10.3934/proc.2007.2007.667 |
[10] |
Kousuke Kuto. Stability and Hopf bifurcation of coexistence steady-states to an SKT model in spatially heterogeneous environment. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 489-509. doi: 10.3934/dcds.2009.24.489 |
[11] |
Lijuan Wang, Hongling Jiang, Ying Li. Positive steady state solutions of a plant-pollinator model with diffusion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1805-1819. doi: 10.3934/dcdsb.2015.20.1805 |
[12] |
Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen. Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation. Evolution Equations and Control Theory, 2015, 4 (1) : 39-59. doi: 10.3934/eect.2015.4.39 |
[13] |
La-Su Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 981-1004. doi: 10.3934/dcds.2016.36.981 |
[14] |
Mei-hua Wei, Jianhua Wu, Yinnian He. Steady-state solutions and stability for a cubic autocatalysis model. Communications on Pure and Applied Analysis, 2015, 14 (3) : 1147-1167. doi: 10.3934/cpaa.2015.14.1147 |
[15] |
Qilong Zhai, Ran Zhang. Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 403-413. doi: 10.3934/dcdsb.2018091 |
[16] |
Juntang Ding, Xuhui Shen. Upper and lower bounds for the blow-up time in quasilinear reaction diffusion problems. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4243-4254. doi: 10.3934/dcdsb.2018135 |
[17] |
Christoph Kawan. Upper and lower estimates for invariance entropy. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 169-186. doi: 10.3934/dcds.2011.30.169 |
[18] |
Robert Elliott, Dilip B. Madan, Tak Kuen Siu. Lower and upper pricing of financial assets. Probability, Uncertainty and Quantitative Risk, 2022, 7 (1) : 45-66. doi: 10.3934/puqr.2022004 |
[19] |
João Fialho, Feliz Minhós. The role of lower and upper solutions in the generalization of Lidstone problems. Conference Publications, 2013, 2013 (special) : 217-226. doi: 10.3934/proc.2013.2013.217 |
[20] |
Luisa Malaguti, Cristina Marcelli. Existence of bounded trajectories via upper and lower solutions. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 575-590. doi: 10.3934/dcds.2000.6.575 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]