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2014, 11(3): 511-521. doi: 10.3934/mbe.2014.11.511

## Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population

 1 Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, United States

Received  January 2013 Revised  June 2013 Published  January 2014

To determine optimal sterile insect release policies in area-wide integrated pest management is a challenge that users of this pest control method inevitably confront. In this note we provide approximations to best policies of release through the use of simulated annealing. The discrete time model for the population dynamics includes the effects of sterile insect release and density dependence in the pest population. Spatial movement is introduced through integrodifference equations, which allow the use of the stochastic search in cases where movement is described through arbitrary dispersal kernels. As a byproduct of the computations, an assessment of appropriate control zone sizes is possible.
Citation: 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
##### References:
 [1] A. Bakri, K. Mehta and D. R. Lance, Sterilizing insects with ionizing radiation,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 233. doi: 10.1007/1-4020-4051-2_9. [2] H. J. Barclay, The sterile release method with unequal male competitive ability,, Ecological Modelling, 15 (1982), 251. doi: 10.1016/0304-3800(82)90029-1. [3] H. J. Barclay, Modelling the effects of aggregation on the efficiency of insect pest control,, Researches on Population Ecology, 34 (1992), 131. doi: 10.1007/BF02513526. [4] H. J. Barclay, Modeling incomplete sterility in a sterile release program: interactions with other factors,, Researches on Population Ecology, 43 (2001), 197. doi: 10.1007/s10144-001-8183-7. [5] H. J. Barclay, Mathematical models for the use of sterile insects,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 147. doi: 10.1007/1-4020-4051-2_6. [6] H. J. Barclay and M. Mackauer, The sterile insect release method for pest control: a density-dependent model,, Environmental Entomology, 9 (1980), 810. [7] H. J. Barclay, R. Matlock, S. Gilchrist, D. M. Suckling, J. Reyes, W. R. Enkerlin and M. J. B. Vreysen, A conceptual model for assessing the minimum size area for an area-wide integrated pest management program,, International Journal of Agronomy, 2011 (4093). doi: 10.1155/2011/409328. [8] W. G. Costello and H. M. Taylor, Mathematical models of the sterile male technique of insect control,, in Mathematical Analysis of Decision Problems in Ecology (eds. A. Charnes and W. R. Lynn). Lecture Notes in Biomathematics, 5 (1975), 318. doi: 10.1007/978-3-642-80924-8_12. [9] F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation,, Oxford University Press, (2008). doi: 10.1093/acprof:oso/9780198570301.001.0001. [10] W. Danthanarayana, Population Ecology of the Light Brown Apple Moth, Epiphyas postvittana (Lepidoptera: Tortricidae),, Journal of Animal Ecology, 52 (1983), 1. doi: 10.2307/4585. [11] W. R. Enkerlin, Impact of fruit fly control programmes using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 651. doi: 10.1007/1-4020-4051-2_25. [12] W. Enkerlin, Guidance for packing, shipping, holding and release of sterile flies in area-wide fruit fly control programmes,, Joint FAO/IAEA progamme of nuclear techniques in food and agriculture. Food and Agriculture Organization of the United Nations, (2007). [13] O. Häggström, Finite Markov Chains and Algorithmic Applications,, Cambridge University Press, (2003). doi: 10.1017/CBO9780511613586. [14] K. Klassen and C. F. Curtis, History of the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 3. doi: 10.1007/1-4020-4051-2_1. [15] E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males,, Journal of Economic Entomology, 48 (1953), 459. [16] M. Kot, M. A. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms,, Ecology, 77 (1996), 2027. doi: 10.2307/2265698. [17] M. F. L'Annunziata, Radioactivity: Introduction and History,, Elsevier, (2007). [18] M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release,, Mathematical Biosciences, 116 (1993), 221. doi: 10.1016/0025-5564(93)90067-K. [19] J. D. Mumford J.D., Applications of benefit/cost analysis to insect pest control using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 481. [20] M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern formation in a discrete-time predator-prey model,, Theoretical Population Biology, 48 (1995), 7. [21] S. L. Peck and J. Bouyer, Mathematical modeling, spatial complexity, and critical decisions in Tsetse control,, Journal of Economic Entomology, 105 (2012), 1477. doi: 10.1603/EC12067. [22] T. Prout, The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population,, Theoretical Population Biology, 13 (1978), 40. doi: 10.1016/0040-5809(78)90035-7. [23] D. Suckling, J. F. Brunner, G. M. Burnip and J. T. S. Walker, Dispersal of Epiphyas postvittana (Walker) and Planotortrix octo Dugdale (Lepidoptera: Tortricidae) at a Canterbury, New Zealand orchard,, New Zealand Journal of Crop and Horticultural Science, 22 (1994), 225. [24] R. A. J. Taylor, The relationship between density and distance of dispersing insects,, Ecological Entomology, 3 (1978), 63. doi: 10.1111/j.1365-2311.1978.tb00903.x. [25] G. M. Viswanathan, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, The Physics of Foraging,, Cambridge University Press, (2011). [26] M-H Wang, M. Kot and M. G. Neubert, Integrodifference equations, Allee effects, and invasions,, Journal of Mathematical Biology, 44 (2002), 150. doi: 10.1007/s002850100116. [27] T. Yamanaka and A. M. Liebhold, Spatially implicit approaches to understand the manipulation of mating success for insect invasion management,, Population Ecology, 51 (2009), 427. doi: 10.1007/s10144-009-0155-3.

show all references

##### References:
 [1] A. Bakri, K. Mehta and D. R. Lance, Sterilizing insects with ionizing radiation,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 233. doi: 10.1007/1-4020-4051-2_9. [2] H. J. Barclay, The sterile release method with unequal male competitive ability,, Ecological Modelling, 15 (1982), 251. doi: 10.1016/0304-3800(82)90029-1. [3] H. J. Barclay, Modelling the effects of aggregation on the efficiency of insect pest control,, Researches on Population Ecology, 34 (1992), 131. doi: 10.1007/BF02513526. [4] H. J. Barclay, Modeling incomplete sterility in a sterile release program: interactions with other factors,, Researches on Population Ecology, 43 (2001), 197. doi: 10.1007/s10144-001-8183-7. [5] H. J. Barclay, Mathematical models for the use of sterile insects,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 147. doi: 10.1007/1-4020-4051-2_6. [6] H. J. Barclay and M. Mackauer, The sterile insect release method for pest control: a density-dependent model,, Environmental Entomology, 9 (1980), 810. [7] H. J. Barclay, R. Matlock, S. Gilchrist, D. M. Suckling, J. Reyes, W. R. Enkerlin and M. J. B. Vreysen, A conceptual model for assessing the minimum size area for an area-wide integrated pest management program,, International Journal of Agronomy, 2011 (4093). doi: 10.1155/2011/409328. [8] W. G. Costello and H. M. Taylor, Mathematical models of the sterile male technique of insect control,, in Mathematical Analysis of Decision Problems in Ecology (eds. A. Charnes and W. R. Lynn). Lecture Notes in Biomathematics, 5 (1975), 318. doi: 10.1007/978-3-642-80924-8_12. [9] F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation,, Oxford University Press, (2008). doi: 10.1093/acprof:oso/9780198570301.001.0001. [10] W. Danthanarayana, Population Ecology of the Light Brown Apple Moth, Epiphyas postvittana (Lepidoptera: Tortricidae),, Journal of Animal Ecology, 52 (1983), 1. doi: 10.2307/4585. [11] W. R. Enkerlin, Impact of fruit fly control programmes using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 651. doi: 10.1007/1-4020-4051-2_25. [12] W. Enkerlin, Guidance for packing, shipping, holding and release of sterile flies in area-wide fruit fly control programmes,, Joint FAO/IAEA progamme of nuclear techniques in food and agriculture. Food and Agriculture Organization of the United Nations, (2007). [13] O. Häggström, Finite Markov Chains and Algorithmic Applications,, Cambridge University Press, (2003). doi: 10.1017/CBO9780511613586. [14] K. Klassen and C. F. Curtis, History of the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 3. doi: 10.1007/1-4020-4051-2_1. [15] E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males,, Journal of Economic Entomology, 48 (1953), 459. [16] M. Kot, M. A. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms,, Ecology, 77 (1996), 2027. doi: 10.2307/2265698. [17] M. F. L'Annunziata, Radioactivity: Introduction and History,, Elsevier, (2007). [18] M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release,, Mathematical Biosciences, 116 (1993), 221. doi: 10.1016/0025-5564(93)90067-K. [19] J. D. Mumford J.D., Applications of benefit/cost analysis to insect pest control using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 481. [20] M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern formation in a discrete-time predator-prey model,, Theoretical Population Biology, 48 (1995), 7. [21] S. L. Peck and J. Bouyer, Mathematical modeling, spatial complexity, and critical decisions in Tsetse control,, Journal of Economic Entomology, 105 (2012), 1477. doi: 10.1603/EC12067. [22] T. Prout, The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population,, Theoretical Population Biology, 13 (1978), 40. doi: 10.1016/0040-5809(78)90035-7. [23] D. Suckling, J. F. Brunner, G. M. Burnip and J. T. S. Walker, Dispersal of Epiphyas postvittana (Walker) and Planotortrix octo Dugdale (Lepidoptera: Tortricidae) at a Canterbury, New Zealand orchard,, New Zealand Journal of Crop and Horticultural Science, 22 (1994), 225. [24] R. A. J. Taylor, The relationship between density and distance of dispersing insects,, Ecological Entomology, 3 (1978), 63. doi: 10.1111/j.1365-2311.1978.tb00903.x. [25] G. M. Viswanathan, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, The Physics of Foraging,, Cambridge University Press, (2011). [26] M-H Wang, M. Kot and M. G. Neubert, Integrodifference equations, Allee effects, and invasions,, Journal of Mathematical Biology, 44 (2002), 150. doi: 10.1007/s002850100116. [27] T. Yamanaka and A. M. Liebhold, Spatially implicit approaches to understand the manipulation of mating success for insect invasion management,, Population Ecology, 51 (2009), 427. doi: 10.1007/s10144-009-0155-3.

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