Impulsive spatial control of invading pests by generalist predators

Mathematical Medicine and Biology

Volumn 31, Issue 3, 2014, Pages 284-301

  Aniţa, Sebastian ^a   Casas, Jérôme ^b   Suppo, Christelle ^b  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

^b UNIVERSITÉ DE TOURS   (France)

Author keywords

Eigenvalue problem; Generalist predator; Host parasitoid; Impulsive control; Integro partial differential equations; Invasion biology; Pest control

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

EIGENVALUE PROBLEM; GENERALIST PREDATORS; HOST-PARASITOID; IMPULSIVE CONTROLS; INTEGRO-PARTIAL DIFFERENTIAL EQUATION; INVASION BIOLOGY; LEAFMINERS; PEST ERADICATION; PRINCIPAL EIGENVALUES; SPATIAL CONTROL;

PARTIAL DIFFERENTIAL EQUATIONS;

AESCULUS; ANIMAL; BIOLOGICAL PEST CONTROL; GROWTH, DEVELOPMENT AND AGING; LEPIDOPTERA; PARASITOLOGY; PLANT LEAF; PREDATION; PROCEDURES; THEORETICAL MODEL;

AESCULUS; ANIMALS; LEPIDOPTERA; MODELS, THEORETICAL; PEST CONTROL, BIOLOGICAL; PLANT LEAVES; PREDATORY BEHAVIOR;

EID: 84907990090     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: 10.1093/imammb/dqt011     Document Type: Article

References (49)

1. Ainseba, B. & Aniţa, S. (2005) Internal stabilizability for a reaction-diffusion problem modeling a predator-prey system. Nonlinear Anal. Theory Meth. Appl., 61, 491-501
2. Aniţa, S. & Capasso, V. (2009) A stabilization strategy for a reaction-diffusion system modelling a class of spatially structured epidemic systems (think globally, act locally). Nonlinear. Anal. Real World Appl., 10, 2026-2035
3. Aniţa, S. & Capasso, V. (2011) Stabilization or a reaction-diffusion system modelling a class of spatially structured epidemic systems The periodic case. Advances in Dynamics and Control: Theory, Methods, and Applications (S. Sivasundaram, J. V. Devi, F. E. Udwadia & I. Lasiecka eds). Cambridge: Cambridge Scientific Publishers Ltd., pp. 181-194
4. Aniţa, S., Fitzgibbon, W. E. & Langlais, M. (2009) Global existence and internal stabilization for a class of predator-prey systems posed on non-coincident spatial domains. Discrete Contin. Dyn. Syst. Ser. B, 11, 805-822
5. Augustin, S. & Reynaud, P. (2000) Un nouveau ravageur pour le marronier: Cameraria ohridella. PHM Revue Horticole, 418, 41-45
6. Balder, H. & Jäckel, B. (2003) Bekämpfungsansätze der Kastanienmimiermotte in Berlin. Nachrichtenbl. Deut Pflanzenschutzd, 55, 221-226
7. Capasso, V. (2009) Mathematical Structures of Epidemic Systems, 2nd revised printing. Heidelberg: Springer
8. Chen, Y., Liu, Z. & Qin, W. (2010) Modelling and analysis of a pest-control pollution model with integrated control tactics. Discrete Dyn. Nat. Soc., 2010, 21 pp
9. Coville, J. (2010) On a simple criterion for the existence of a principal eigenfunction of some nonlocal operator. J. Differential Equations, 249, 2921-2953
10. Deimling, K. (1985) Nonlinear Functional Analysis. Berlin: Springer
11. Deschka, G. (1993) DieMiniermotte Cameraria ohridella DESCHKA & DIMIC eine Gefahr für die Rosskastanie Aesculus hippocastanum L. (Insecta, Lepidoptera, Lithocolletidae). Linzer Biol. Beitr., 25, 141-148
12. Deschka, G. & Dimic, N. (1986) Cameraria ohridella sp.n. (Lepidoptera, Lithocolletidae) aus Mazedonien, Jugoslawien. Acta Entomol. Jugosl., 22, 11-23
13. Ferracini, C. & Alma, A. (2008) How to preserve horse chestnut tree from Cameraria ohridella in the urban environment. Crop Protect., 27, 1251-1255
14. Fitzgibbon, W. E. & Langlais, M. (2008) Simple models for transmission of microparasites between host populations living on noncoincident spatial domains. Structured Population Models in Biology and Epidemiology (P. Magal & S. Ruan eds), Chapter 3. Berlin: Springer, pp. 115-164
15. Freise, J. F., Heitland,W. & Tosevski, I. (2002) Parasitism of the horse chestnut leaf miner, Cameraria ohridella Deschka and Dimic (Lep., Gracillariidae), in Serbia and Macedonia. J. Pest Sci., 75, 151-157
16. Friedman, A. (1964) Partial Differential Equations of Parabolic Type. Englewood Cliffs, NJ: Prentice-Hall
17. Genieys, S., Volpert, V. & Auge, P. (2006) Pattern and waves for a model in population dynamics with nonlocal consumption of resources. Math. Mod. Nat. Phenom., 1, 65-82
18. Gilbert,M., Gregoire, J.-C., Freise, J.-F. & Heitland,W. (2004) Long-distance dispersal and human population density allow the prediction of invasive patterns in the horsechestnut leafminer Cameraria ohridella. J. Anim Ecol., 73, 459-468
19. Gilbert, M., Guichard, S., Freise, J.-F., Gregoire, J.-C., Heitland, W., Straw, N., Tilbury, C. & Augustin, S. (2005) Forecasting Cameraria ohridella invasion dynamics in recently invaded countries: from validation to prediction. J. Appl. Ecol., 42, 805-813
20. Gilbert, M., Svatoš, A., Lehmann, M. & Bacher, S. (2003) Spatial patterns & infestation processes in the horse chestnut leafminer Cameraria ohridella: a tale of two cities. Entomol. Exp. Appl., 107, 25-37
21. Girardoz, S., Volter, L., Tomov, R., Quicke, D. L. J. & Kenis, M. (2007) Variations in parasitism in sympatric populations of three invasive leaf miners. J. Appl. Entomol., 131, 603-612
22. Grabenweger, G. & Grill, R. (2000) On the place of origin of Cameraria ohridella Deschka and Dimic (Lepidoptera: Gracillariidae). Beitr. Entomofaun, 1, 9-17
23. Grabenweger, G., Kehrli, P., Zweimüller, I., Augustin, S., Avtzis, N., Bacher, S., Freise, J., Girardoz, S., Guichard, S., Heitland, W., Lethmayer, C., Stolz, M., Tomov, R., Volter, L. & Kenis, M. (2010) Temporal and spatial variations in the parasitoid complex of the horse chestnut leafminer during its invasion of Europe. Biol. Invasions, 12, 2797-2813
24. Grasman, J., van Herwaarden, O. A., Hemerik, L. & van Lenteren, J. C. (2001) A two component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control. Math. Biosci., 169, 207-216
25. Greenman, J. V. & Norman, R. A. (2007) Environmental forcing, invasion and control of ecological and epidemiological systems. J. Theoret. Biol., 247, 492-506
26. Guichard, S. & Augustin, S. (2002) Acute spread in France of an European invasive pest, Cameraria ohridella Deschka & Dimic (Lepidoptera, Gracillariidae). J. Pest Sci., 75, 145-149
27. Heitland, W., Kopelke, J.-P., Freise, J. & Metzger, J. (1999) Ein kleinschmetterling erobert Europa-die rosskastanien-miniermotte Cameraria ohridella. Natur und Museum, 129, 186-195
28. Kehrli, P. & Bacher, S. (2003) Date of leaf litter removal to prevent emergence of Cameraria ohridella in the following spring. Entomol. Exp. Appl., 107, 159-162
29. Kehrli, P., Lehmann, M. & Bacher, S. (2005) Mass-emergence devices: a biocontrol technique for conservation and augmentation of parasitoids. Biol. Control, 32, 191-199
30. Kehrli, P. & Bacher, S. (2004) How to safety compost Cameraria ohridella-infested horse chestnut leaf litter on private heaps. J. Appl. Entomol., 128, 707-709
31. Kobza, M., Juhásová, G., Adamčíková, K. & Onrušková, E. (2011) Tree injection in the management of horse-chestnut leaf miner Cameraria ohridella (Lepidoptera: Gracillariidae). Gesunde Pflanzen, 62, 139-143
32. Krehan, H. (1995) Roßkastanienminiermotte-befallssituation in Österreich. Forstschutz-Aktuell, Wien, 16, 8-11
33. Lions, J. L. (1988) Controlabilité Exacte, Stabilisation et Perturbation de Systèmes Distribué. Paris: Masson
34. Magal, C., Cosner, C., Ruan, S. & Casas, J. (2008) Control of invasive hosts by generalist parasitoids. Math Med. Biol., 25, 1-20
35. Percival, G. C., Barrow, I., Noviss, K., Keary, I. & Pennington, P. (2011) The impact of horse chestnut leaf miner (Cameraria ohridella Deschka and Dimic; HCLM) on vitality, growth and reproduction of Aesculus hippocastaneum L. Urban Forestry Urban Greening, 10, 11-17
36. Protter, M. H. &Weinberger, H. F. (1984) Maximum Principles in Differential Equations. New York: Springer
37. Sefrova, H. & Lastuvka, Z. (2001) Dispersal of the horse-chestnut leafminer, Cameraria ohridella in Europe: its course, ways and causes. Entomol. Zeit Stuggart, 111, 195-198
38. Siekmann, G., Meyhöfer, R. & Hommes, M. (2009) Testing mating disruption of the horse chestnut leafminer Cameraria ohridella (Lepidoptera: Gracillariidae) in field tents. J. Pest Sci., 82, 129-136
39. Simova-Tosic, D. & Filev, S. (1985) Contribution to the horse chestnut miner. Zastita Bilja, 36, 235-239
40. Srinivasu, P. D. N. & Prasad, B. S. R. V. (2011) Role of quantity of additional food to predators as a control in predator-prey systems with relevance to pest management and biological conservation. Bull. Math. Biol., 73, 2249-2276
41. Straw, N. A. & Tilbury, C. (2006) Host plants of the horse-chestnut leaf-miner (Cameraria ohridella), and the rapid spread of the moth in the UK 2002-2005. Arboricultural J., 29, 83-99
42. Sukovata, L., Czokajlo, D., Kolk, A., Ślusarski, S. & Jabłónski, T. (2011) An attempt to control Cameraria ohridella using an attract-kill technique. J. Pest Sci., 84, 207-212
43. Tang, S., Tang, G. & Cheke, R. A. (2010) Optimum timing for integrated pest management: modelling rates of pesticide application and natural enemy releases. J. Theoret. Biol., 264, 623-638
44. Teng, Z., Nie, L. & Fang, X. (2011) The periodic solutions for general periodic impulsive population systems of functional differential equations and its applications. Comp. Math. Appl., 61, 2690-2703
45. Thalmann, C., Freise, J., Heitland, W. & Bache, S. (2003) Effects of defoliation by horse chestnut leafminer (Cameraria ohridella) on reproduction in Aesculus hippocastanum. Trees, 17, 383-388
46. Tomiczek, C. & Krehan, H. (1998) The horsechestnut leafmining moth (Cameraria ohridella): a new pest in Central Europe. J. Arboriculture, 24, 144-148
47. Turchin, P. (2003) Complex Population Dynamics: A Theoretical/Empirical Synthesis, Monographs in Population Biology. Princeton, NJ: Princeton University Press
48. Yang, T. (2001) Impulsive Control Theory. Lecture Notes in Control and Information Science, vol. 272. Berlin: Springer
49. Zunke, U., Fernandez-Nunez, M., Ilmberger, N., Hofmeier, M., Konitz, K. & Doobe, G. (2006) Cameraria ohridella. HAM-CAM Projekt 2011/04, Hamburg