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Mathematical modelling of the sterile insect technique using different release strategies. (English) Zbl 1459.92073
Summary: We study simple mathematical models for the dynamics of interactive wild and sterile insect populations. As well as being mathematically tractable, these models can be used as first approximations to real situations occurring with the Sterile Insect Technique (SIT) in which sterile males are released to reduce or eradicate a pest population. This is a method of biological control which can effectively help contain the spread of many pest insects such as the Red Palm Weevil (RPW). Models formulated in this paper are continuous-time, include a strong Allee effect that captures extinction events, and incorporate different strategies of releasing sterile insects. We perform basic studies of dynamical features of these models, with an emphasis on the condition of excitation, and the impact of the different release methods is investigated. Our findings are also demonstrated with some numerical examples.
Reviewer: Reviewer (Berlin)
MSC:
92D25 Population dynamics (general)
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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[1] Knipling, E. F., Possibilities of insect control or eradication through the use of sexually sterile Males1, Journal of Economic Entomology, 48, 4, 459-462 (1955)
[2] Dyck, V. A.; Hendrichs, J.; Robinson, A. S., The Sterile Insect Technique, Principles and Practice in Area-wide Integrated Pest Management (2006), Dordrecht, Netherlands: Springer, Dordrecht, Netherlands
[3] Bourtzis, K., Wolbachia-based Technologies for Insect Pest Population Control: Advances in Experimental Medicine and Biology (2008), New York, NY, USA: Springer, New York, NY, USA
[4] Sinkins, S. P., Wolbachia and cytoplasmic incompatibility in mosquitoes, Insect Biochemistry and Molecular Biology, 34, 7, 723-729 (2004)
[5] Zabalou, S.; Riegler, M.; Theodorakopoulou, M.; Savakis, C.; Bourtzis, K., Wolbachia-induced cytoplasmic incompatibility as a means for insect pest population control, Proceedings of the National Academy of Sciences, 101, 42, 15042-15045 (2004)
[6] Marranzano, M.; Ragusa, R.; Platania, M.; Faro, G.; Coniglio, M. A., Knowledge, attitudes and practices towards patients with HIV/AIDS in staff Nurses in one university hospital in Sicily, Ital. Journal of Public Health, 10, 1, 1-23 (2013)
[7] Nikolouli, K.; Sassù, F.; Mouton, L.; Stauffer, C.; Bourtzis, K., Combining sterile and incompatible insect techniques for the population suppression of Drosophila suzukii, Journal of Pest Science, 93, 2, 647-661 (2020)
[8] Ragusa, R.; Russo, S.; Villari, L.; Schilirò, G., Hodgkin’s disease as a second malignant neoplasm in childhood: report of a case and review of the literature, Pediatric Hematology and Oncology, 18, 6, 407-414 (2001)
[9] Reale, G.; Russo, G. I.; Di Mauro, M., Association between dietary flavonoids intake and prostate cancer risk: a case-control study in Sicily, Complementary Therapies in Medicine, 39, 14-18 (2018)
[10] Stauffer, D.; Lees, R. S.; Xi, Z., Combining the sterile insect technique with Wolbachia-based approaches: II a safer approach to Aedes albopictus population suppression programmes, designed to minimize the consequences of inadvertent female release, PLoS One, 10, 8, 1-26 (2015)
[11] Zhang, D.; Zheng, X.; Xi, Z.; Bourtzis, K.; Gilles, J. R., Combining the sterile insect technique with the incompatible insect technique: I-impact of wolbachia infection on the ftness of triple- and double-infected strains of Aedes albopictus, PLoS One, 10, 4, 1-15 (2015a)
[12] Yen, P.-S.; Failloux, A.-B., A review: wolbachia-based population replacement for mosquito control shares common points with genetically modified control approaches, Pathogens, 9, 5, 404-421 (2020)
[13] Rasgon, J. L.; Scott, T. W., Wolbachia and cytoplasmic incompatibility in the California culex pipiens mosquito species complex: parameter estimates and infection dynamics in natural populations, Genetics, 165, 4, 2029-2038 (2003)
[14] Hoffmann, A. A.; Montgomery, B. L.; Popovici, J., Successful establishment of wolbachia in aedes populations to suppress dengue transmission, Nature, 476, 7361, 454-457 (2011)
[15] Boulaaras, S.; Haiour, M., The finite element approximation of evolutionary Hamilton-Jacobi-Bellman equations with nonlinear source terms, Indagationes Mathematicae, 24, 1, 161-173 (2013) · Zbl 1254.65104
[16] Boulaaras, S.; Haiour, M., L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem, Applied Mathematics and Computation, 217, 14, 6443-6450 (2011) · Zbl 1211.65083
[17] Boulaaras, S., Some existence results for a new class of elliptic kirchhoff equation with logarithmic source terms, Journal of Intelligent & Fuzzy Systems, 37, 6, 8335-8344 (2019)
[18] Boulaaras, S., Some new properties of asynchronous algorithms of theta scheme combined with finite elements methods for an evolutionary implicit 2-sided obstacle problem, Mathematical Methods in the Applied Sciences, 40, 18, 7231-7239 (2017) · Zbl 1380.65252
[19] Boulaaras, S., An optimal error estimate of finite element method for parabolic quasi-variational inequalities with non linear source terms, Asymptotic Analysis, 100, 3-4, 193-208 (2016) · Zbl 1371.65062
[20] Boulaaras, S., Existence of positive solutions for a new class of Kirchhoff parabolic systems, Rocky Mountain Journal of Mathematics, 50, 2, 445-454 (2020) · Zbl 1443.35075
[21] Dufourd, C.; Dumont, Y., Modeling and simulations of mosquito dispersal. the case of Aedes albopictus, Biomath, 1, 2 (2012) · Zbl 1368.92141
[22] Dufourd, C.; Dumont, Y., Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control, Computers & Mathematics with Applications, 66, 9, 1695-1715 (2013) · Zbl 1345.34105
[23] Dumont, Y.; Tchuenche, J. M., Mathematical studies on the sterile insect technique for the chikungunya disease and Aedes albopictus, Journal of Mathematical Biology, 65, 5, 809-855 (2012) · Zbl 1311.92175
[24] Huang, M.; Song, X.; Li, J., Modelling and analysis of impulsive releases of sterile mosquitoes, Journal of Biological Dynamics, 11, 1, 147-171 (2017) · Zbl 1448.92296
[25] Li, J.; Cai, L.; Li, Y., Stage-structured wild and sterile mosquito population models and their dynamics, Journal of Biological Dynamics, 11, 1, 79-101 (2017) · Zbl 1448.92219
[26] Li, J.; Yuan, Z., Modelling releases of sterile mosquitoes with different strategies, Journal of Biological Dynamics, 9, 1, 1-14 (2015) · Zbl 1448.92220
[27] Farkas, J. Z.; Hinow, P., Structured and unstructured continuous models for wolbachia infections, Bulletin of Mathematical Biology, 72, 8, 2067-2088 (2010) · Zbl 1201.92044
[28] Fenton, A.; Johnson, K. N.; Brownlie, J. C.; Hurst, G. D. D., Solving the wolbachia paradox: modeling the tripartite interaction between host, wolbachia, and a natural enemy, The American Naturalist, 178, 3, 333-342 (2011)
[29] Farkas, J. Z.; Gourley, S. A.; Liu, R.; Yakubu, A.-A., Modelling Wolbachia infection in a sex-structured mosquito population carrying west nile virus, Journal of Mathematical Biology, 75, 3, 621-647 (2017) · Zbl 1387.92082
[30] Nadin, G.; Strugarek, M.; Vauchelet, N., Hindrances to bistable front propagation: application to wolbachia invasion, Journal of Mathematical Biology, 76, 6, 1489-1533 (2018) · Zbl 1411.34039
[31] Bendhahbi, A.; Chargui, Y.; Boulaaras, S.; Ben Khalifa, S., A one-sided competition mathematical model for the sterile insect technique, Complexity, 2020 (2020)
[32] Li, J., New revised simple models for interactive wild and sterile mosquito populations and their dynamics, Journal of Biological Dynamics, 11, 2, 316-333 (2017) · Zbl 1448.92217
[33] Courchamp, F.; Clutton-Brock, T.; Grenfell, B., Inverse density dependence and the Allee effect, Trends in Ecology & Evolution, 14, 10, 405-410 (1999)
[34] Gruntfest, Y.; Arditi, R.; Dombrovsky, Y., A fragmented population in a varying environment, Journal of Theoretical Biology, 185, 4, 539-547 (1997)
[35] Walter, J. A.; Grayson, K. L.; Johnson, D. M., Variation in allee effects: evidence, unknowns, and directions forward, Population Ecology, 59, 2, 99-107 (2017)
[36] Courchamp, F.; Berec, L.; Gascoigne, J., Allee Effects in Ecology and Conservation (2008), Oxford, UK: Oxford University Press, Oxford, UK
[37] Ferreira, C. P.; Yang, H. M.; Esteva, L., Assessing the suitability of sterile insect technique applied toaedes aegypti, Journal of Biological Systems, 16, 04, 565-577 (2008)
[38] Kim, J.; Lee, H.; Lee, C.; Lee, S., Assessment of optimal strategies in a two-patch dengue transmission model with seasonality, PLoS One, 12, 3, 1-21 (2017)
[39] Multerer, L.; Smith, T.; Chitnis, N., Modeling the impact of sterile males on an Aedes aegypti population with optimal control, Mathematical Biosciences, 311, 91-102 (2019) · Zbl 1425.92131
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