To study the biological control strategy of aphids, in this paper we propose host-parasitoid-predator models for the interactions among aphids, parasitic wasps and aphidophagous Coccinellids incorporating impulsive releases of Coccinellids, and then study the long-term control and limited time optimal control of aphids by adjusting release amount and release timing of Coccinellids. For the long-term control, the existence and stability of the aphid-eradication periodic solution are investigated and threshold conditions about the release amount and release period to ensure the ultimate extinction of the aphid population are obtained. For the limited-time control, three different optimal impulsive control problems are studied. A time rescaling technique and an optimization algorithm based on gradient are applied, and the optimal release amounts and timings of natural enemies are gained. Our simulations indicate that in the limited-time control, the optimal selection of release timing should be given higher priority compared with the release amount.
Citation: Mingzhan Huang, Shouzong Liu, Ying Zhang. Mathematical modeling and analysis of biological control strategy of aphid population[J]. AIMS Mathematics, 2022, 7(4): 6876-6897. doi: 10.3934/math.2022382
To study the biological control strategy of aphids, in this paper we propose host-parasitoid-predator models for the interactions among aphids, parasitic wasps and aphidophagous Coccinellids incorporating impulsive releases of Coccinellids, and then study the long-term control and limited time optimal control of aphids by adjusting release amount and release timing of Coccinellids. For the long-term control, the existence and stability of the aphid-eradication periodic solution are investigated and threshold conditions about the release amount and release period to ensure the ultimate extinction of the aphid population are obtained. For the limited-time control, three different optimal impulsive control problems are studied. A time rescaling technique and an optimization algorithm based on gradient are applied, and the optimal release amounts and timings of natural enemies are gained. Our simulations indicate that in the limited-time control, the optimal selection of release timing should be given higher priority compared with the release amount.
| [1] | R. Singh, G. Singh, Aphids and their biocontrol, New York: Academic Press, 2016, 63–108. https://doi.org/10.1016/B978-0-12-803265-7.00003-8 |
| [2] |
B. Zheng, J. Yu, J. Li, Modeling and analysis of the implementation of the Wolbachia incompatible and sterile insect technique for mosquito population suppression, SIAM J. Appl. Math., 81 (2021), 718–740. https://doi.org/10.1137/20M1368367 doi: 10.1137/20M1368367
|
| [3] |
B. Zheng, J. Yu, Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency, Adv. Nonlinear Anal., 11 (2022), 212–224. https://doi.org/10.1515/anona-2020-0194 doi: 10.1515/anona-2020-0194
|
| [4] | B. Zheng, J. Li, J. Yu, One discrete dynamical model on Wolbachia infection frequency in mosquito populations, Sci. China Math., 2021. https://doi.org/10.1007/s11425-021-1891-7 |
| [5] |
E. W. Evans, Multitrophic interactions among plants, aphids, alternate prey and shared natural enemies-a review, Eur. J. Entomol., 105 (2008), 369–380. https://doi.org/10.14411/eje.2008.047 doi: 10.14411/eje.2008.047
|
| [6] | G. A. Polis, C. A. Myers, R. D. Holt, The ecology and evolution of intraguild predation: Potential competitors that eat each other, Annu. Rev. Ecol. Sys., 20 (1989), 297–330. |
| [7] |
J. A. Rosenheim, H. K. Kaya, L. E. Ehler, J. J. Marois, B. A. Jaffee, Intraguild predation among biological-control agents: Theory and evidence, Biol. Control, 5 (1995), 303–335. https://doi.org/10.1006/bcon.1995.1038 doi: 10.1006/bcon.1995.1038
|
| [8] |
J. Brodeur, J. A. Rosenheim, Intraguild interactions in aphid parasitoids, Entomol. Exp. Appl., 97 (2000), 93–108. https://doi.org/10.1046/j.1570-7458.2000.00720.x doi: 10.1046/j.1570-7458.2000.00720.x
|
| [9] |
R. G. Colfer, J. A. Rosenheim, Predation on immature parasitoids and its impact on aphid suppression, Oecologia, 126 (2001), 292–304. https://doi.org/10.1007/s004420000510 doi: 10.1007/s004420000510
|
| [10] | W. E. Snyder, A. R. Ives, Generalist predators disrupt biological control by a specialist parasitoid, Ecology, 82 (2001), 705–716. |
| [11] |
E. Bilu, M. Coll, The importance of intraguild interactions to the combined effect of a parasitoid and a predator on aphid population suppression, Biocontrol, 52 (2007), 753–763. https://doi.org/10.1007/s10526-007-9071-7 doi: 10.1007/s10526-007-9071-7
|
| [12] |
L. M. Gontijo, E. H. Beers, W. E. Snyder, Complementary suppression of aphids by predators and parasitoids, Biol. Control, 90 (2015), 83–91. https://doi.org/10.1016/j.biocontrol.2015.06.002 doi: 10.1016/j.biocontrol.2015.06.002
|
| [13] |
T. Nakazawa, N. Yamamura, Community structure and stability analysis for intraguild interactions among host, parasitoid, and predator, Popul. Ecol., 48 (2006), 139–149. https://doi.org/10.1007/s10144-005-0249-5 doi: 10.1007/s10144-005-0249-5
|
| [14] |
X. Y. Liang, Y. Z. Pei, M. X. Zhu, Y. F. Lv, Multiple kinds of optimal impulse control strategies on plant-pest-predator model with eco-epidemiology, Appl. Math. Comput., 287-288 (2016), 1–11. https://doi.org/10.1016/j.amc.2016.04.034 doi: 10.1016/j.amc.2016.04.034
|
| [15] |
Y. Z. Pei, M. M. Chen, X. Y. Liang, C. G. Li, X. Z. Meng, Optimizing pulse timings and amounts of biological interventions for a pest regulation model, Nonlinear Anal.-Hybrid Syst., 27 (2018), 353–365. https://doi.org/10.1016/j.nahs.2017.10.003 doi: 10.1016/j.nahs.2017.10.003
|
| [16] | S. Z. Liu, L. Yu, M. Z. Huang, X. Shi, Studies on the optimization selection of injection timings and injection doses based on the integrated control effect of glucose, J. Xinyang Normal Univ. (Nat. Sci. Edit.), 33 (2020), 345–350. |
| [17] |
M. Z. Huang, S. Z. Liu, X. Y. Song, Study of the sterile insect release technique for a two-sex mosquito population model, Math. Biosci. Eng., 18 (2021), 1314–1339. https://doi.org/10.3934/mbe.2021069 doi: 10.3934/mbe.2021069
|
| [18] |
M. Z. Huang, L. You, S. Z. Liu, X. Y. Song, Impulsive release strategies of sterile mosquitos for optimal control of wild population, J. Biol. Dyn., 15 (2021), 151–176. https://doi.org/10.1080/17513758.2021.1887380 doi: 10.1080/17513758.2021.1887380
|
| [19] | D. Bainov, P. Simeonov, Impulsive differential equations: Periodic solutions and applications, 1 Ed., New York: Routledge, 1993. https://doi.org/10.1201/9780203751206 |
| [20] | A. Zhao, W. Yan, J. Yan, Existence of positive periodic solution for an impulsive delay differential equation, Singapore: World Scientific, 2003. https://doi.org/10.1142/9789812704283_0029 |
| [21] |
X. Y. Song, Z. Y. Xiang, The prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects, J. Theor. Biol., 242 (2006), 683–698. https://doi.org/10.1016/j.jtbi.2006.05.002 doi: 10.1016/j.jtbi.2006.05.002
|
| [22] |
M. Z. Huang, J. X. Li, X. Y. Song, H. J. Guo, Modeling impulsive injections of insulin analogues: Towards artificial pancreas, SIAM J. Appl. Math., 72 (2012), 1524–1548. https://doi.org/10.1137/110860306 doi: 10.1137/110860306
|
| [23] |
Y. Liu, K. L. Teo, L. S. Jennings, S. Wang, On a class of optimal control problems with state jumps, J. Optim. Theory Appl., 98 (1998), 65–82. https://doi.org/10.1023/A:1022684730236 doi: 10.1023/A:1022684730236
|
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Mingzhan Huang, Shouzong Liu, Ying Zhang. Mathematical modeling and analysis of biological control strategy of aphid population[J]. AIMS Mathematics, 2022, 7(4): 6876-6897. doi: 10.3934/math.2022382
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