{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T13:54:51Z","timestamp":1791467691600,"version":"4.3.4"},"reference-count":72,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T00:00:00Z","timestamp":1790121600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T00:00:00Z","timestamp":1790121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The sterile insect technique (SIT) is a biological control method aimed at reducing or eliminating populations of pests and disease vectors. This technique involves releasing sterilised insects which, by mating with wild individuals, will reduce the target population. In this study, spatial aspects are incorporated through an explicit metapopulation model, in which both wild and sterile insects disperse across multiple patches. We derive a general sufficient condition ensuring elimination of the wild population in all patches through SIT. When a strong Allee effect is naturally present in each patch, the release programme can be terminated after a finite time, and an upper bound on the required release duration is provided. We then study an optimisation problem aimed at minimising the daily number of sterile insects released to ensure population elimination, under the constraint that the releases occur only in a prescribed subset of patches. For illustrative purposes, we explore through numerical simulations different dispersal network configurations. We also consider additional control by mass trapping (MT), which can affect the sterile insects entering trapped areas. The main contribution of this work is to enable the identification of the best spatial strategies for releasing sterile insects under practical constraints, in order to achieve population elimination.<\/jats:p>","DOI":"10.1007\/s11538-026-01722-3","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T13:27:50Z","timestamp":1790170070000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sterile Insect Technique in a n-patch System with Allee Effect and Mass Trapping: Modelling, Analysis and Simulations"],"prefix":"10.1007","volume":"88","author":[{"given":"Pierre-Alexandre","family":"Bliman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manon","family":"de la Tousche","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4817-685X","authenticated-orcid":false,"given":"Yves","family":"Dumont","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,23]]},"reference":[{"key":"1722_CR1","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/j.jde.2021.12.002","volume":"311","author":"L Almeida","year":"2022","unstructured":"Almeida L, Duprez M, Privat Y, Vauchelet N (2022) Optimal control strategies for the sterile mosquitoes technique. J Differ Equ 311:229\u2013266","journal-title":"J Differ Equ"},{"issue":"3","key":"1722_CR2","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1016\/j.camwa.2012.02.068","volume":"64","author":"R Anguelov","year":"2012","unstructured":"Anguelov R, Dumont Y, Lubuma J (2012) Mathematical modeling of sterile insect technology for control of anopheles mosquito. Comput Math Appl 64(3):374\u2013389","journal-title":"Comput Math Appl"},{"issue":"18","key":"1722_CR3","doi-asserted-by":"publisher","first-page":"10391","DOI":"10.1002\/mma.6385","volume":"43","author":"R Anguelov","year":"2020","unstructured":"Anguelov R, Dumont Y, Yatat Djeumen IV (2020) Sustainable vector\/pest control using the permanent sterile insect technique. Math Methods Appl Sci 43(18):10391\u201310412","journal-title":"Math Methods Appl Sci"},{"issue":"8","key":"1722_CR4","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1007\/s11538-020-00790-3","volume":"82","author":"MS Aronna","year":"2020","unstructured":"Aronna MS, Dumont Y (2020) On nonlinear pest\/vector control via the sterile insect technique: Impact of residual fertility. Bull Math Biol 82(8):110","journal-title":"Bull Math Biol"},{"key":"1722_CR5","unstructured":"Baker R, Gilioli G, Candiani D, Behring C, Gogin A, Kaluski T, Kinkar M, Mosbach-Schulz O, Neri FM, Preti S, Rosace MC, Siligat R, Stancanelli G, Tramontini v (2019)\u201cBactrocera dorsalis \u2013 Pest report and datasheet to support ranking of EU candidate priority pests,\u201d. European Food Safety Authority"},{"key":"1722_CR6","doi-asserted-by":"crossref","unstructured":"Bang-Jensen J, Gutin GZ (2008) Digraphs: theory, algorithms and applications. Springer Science & Business Media","DOI":"10.1007\/978-1-84800-998-1"},{"key":"1722_CR7","doi-asserted-by":"crossref","unstructured":"Barclay H (2021) \u201cMathematical models for using sterile insects,\u201d in Sterile insect technique, pp.\u00a0201\u2013244, CRC Press","DOI":"10.1201\/9781003035572-7"},{"issue":"2","key":"1722_CR8","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/BF02513554","volume":"33","author":"HJ Barclay","year":"1991","unstructured":"Barclay HJ, Haniotakis GE (1991) Combining pheromone-baited and food-baited traps for insect pest control: effects of developmental period. Popul Ecol 33(2):269\u2013285","journal-title":"Popul Ecol"},{"issue":"6","key":"1722_CR9","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1093\/ee\/9.6.810","volume":"9","author":"H Barclay","year":"1980","unstructured":"Barclay H, Mackauer M (1980) The sterile insect release method for pest control: a density-dependent model. Environ Entomol 9(6):810\u2013817","journal-title":"Environ Entomol"},{"key":"1722_CR10","doi-asserted-by":"crossref","unstructured":"Berman A, Plemmons R (1994) Nonnegative matrices in the mathematical sciences. SIAM,","DOI":"10.1137\/1.9781611971262"},{"issue":"8","key":"1722_CR11","doi-asserted-by":"publisher","first-page":"858","DOI":"10.4039\/Ent99858-8","volume":"99","author":"AA Berryman","year":"1967","unstructured":"Berryman AA (1967) Mathematical description of the sterile male principle1. Can Entomol 99(8):858\u2013865","journal-title":"Can Entomol"},{"key":"1722_CR12","doi-asserted-by":"crossref","unstructured":"Bhaya A, Bliman P-A (2025) \u201cFeedback design for biological control by the sterile insect release technique exploiting monotone system theory,\u201d European Journal of Control, p.\u00a0101292","DOI":"10.1016\/j.ejcon.2025.101292"},{"key":"1722_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2022.108856","volume":"350","author":"P-A Bliman","year":"2022","unstructured":"Bliman P-A, Dumont Y (2022) Robust control strategy by the sterile insect technique for reducing epidemiological risk in presence of vector migration. Math Biosci 350:108856","journal-title":"Math Biosci"},{"key":"1722_CR14","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.mbs.2019.06.002","volume":"314","author":"P-A Bliman","year":"2019","unstructured":"Bliman P-A, Cardona-Salgado D, Dumont Y, Vasilieva O (2019) Implementation of control strategies for sterile insect techniques. Math Biosci 314:43\u201360","journal-title":"Math Biosci"},{"issue":"5","key":"1722_CR15","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/s10958-024-07042-y","volume":"279","author":"P-A Bliman","year":"2024","unstructured":"Bliman P-A, Cardona-Salgado D, Dumont Y, Vasilieva O (2024) Optimal control approach for implementation of sterile insect techniques. J Math Sci 279(5):607\u2013622","journal-title":"J Math Sci"},{"key":"1722_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2024.109290","volume":"377","author":"P-A Bliman","year":"2024","unstructured":"Bliman P-A, Nguyen N, Vauchelet N (2024) Efficacy of the sterile insect technique in the presence of inaccessible areas: a study using two-patch models. Math Biosci 377:109290","journal-title":"Math Biosci"},{"key":"1722_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2025.116047","volume":"144","author":"P-A Bliman","year":"2025","unstructured":"Bliman P-A, de la Tousche M, Dumont Y (2025) Feasibility and optimisation results for elimination by mass trapping in a metapopulation model. Appl Math Model 144:116047","journal-title":"Appl Math Model"},{"key":"1722_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex optimization","author":"S Boyd","year":"2004","unstructured":"Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press"},{"key":"1722_CR19","unstructured":"Bullo F, Cort\u00e9s J, D\u00f6rfler F, Mart\u00ednez S (2018) Lectures on network systems, vol 1. CreateSpace,"},{"key":"1722_CR20","doi-asserted-by":"crossref","unstructured":"Burrack HJ, Fornell AM, Connell JH, O\u2019Connell NV, Phillips PA, Vossen PM, Zalom FG (2009) Intraspecific larval competition in the olive fruit fly (Diptera: tephritidae). Environ Entomol 38(5):1400\u20131410","DOI":"10.1603\/022.038.0508"},{"issue":"6","key":"1722_CR21","doi-asserted-by":"publisher","first-page":"1786","DOI":"10.1137\/13094102X","volume":"74","author":"L Cai","year":"2014","unstructured":"Cai L, Ai S, Li J (2014) Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes. SIAM J Appl Math 74(6):1786\u20131809","journal-title":"SIAM J Appl Math"},{"key":"1722_CR22","doi-asserted-by":"crossref","unstructured":"Clarke AR (2019) Biology and management of Bactrocera and related fruit flies. CABI","DOI":"10.1079\/9781789241822.0000"},{"key":"1722_CR23","doi-asserted-by":"crossref","unstructured":"Clarke A, Armstrong K, Carmichael A, Milne J, Raghu S, Roderick G, Yeates D (2005) Invasive phytophagous pests arising through a recent tropical evolutionary radiation: the Bactrocera dorsalis Complex of Fruit Flies. Annu Rev Entomol 50:293\u2013319","DOI":"10.1146\/annurev.ento.50.071803.130428"},{"key":"1722_CR24","unstructured":"Coppel WA (1965) \u201cStability and asymptotic behavior of differential equations,\u201d"},{"key":"1722_CR25","doi-asserted-by":"crossref","unstructured":"Cugala D, Massimiliano V, Maulid M, De Meyer M, Canhanga L (2020) Economic injury level of the Oriental fruit fly, Bactrocera dorsalis (Diptera: Tephritidae), on commercial mango farms in Manica Province, Mozambique. African entomology 28(2):278\u2013289","DOI":"10.4001\/003.028.0278"},{"issue":"4","key":"1722_CR26","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1111\/j.1939-7445.1989.tb00119.x","volume":"3","author":"B Dennis","year":"1989","unstructured":"Dennis B (1989) Allee effects: population growth, critical density, and the chance of extinction. Nat Resour Model 3(4):481\u2013538","journal-title":"Nat Resour Model"},{"issue":"1","key":"1722_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0022-247X(84)90198-7","volume":"102","author":"E Deutsch","year":"1984","unstructured":"Deutsch E, Neumann M (1984) Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an $$M$$-matrix. J Math Anal Appl 102(1):1\u201329","journal-title":"J Math Anal Appl"},{"key":"1722_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecolmodel.2022.109951","volume":"468","author":"EG Diouf","year":"2022","unstructured":"Diouf EG, Br\u00e9vault T, Ndiaye S, Faye E, Chailleux A, Diatta P, Piou C (2022) An agent-based model to simulate the boosted sterile insect technique for fruit fly management. Ecol Model 468:109951","journal-title":"Ecol Model"},{"issue":"9","key":"1722_CR29","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1016\/j.camwa.2013.03.024","volume":"66","author":"C Dufourd","year":"2013","unstructured":"Dufourd C, Dumont Y (2013) Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control. Comput Math Appl 66(9):1695\u20131715","journal-title":"Comput Math Appl"},{"key":"1722_CR30","doi-asserted-by":"crossref","unstructured":"Dumont Y (2025) \u201cOn the improvement of the sterile insect technique by entomopathogenic fungi: impact of residual fertility and re-mating behaviour,\u201d Bulletin of Mathematical Biology, vol.\u00a087, no.\u00a0151","DOI":"10.1007\/s11538-025-01529-8"},{"key":"1722_CR31","doi-asserted-by":"crossref","unstructured":"Dumont Y, Oliva CF (2024) On the impact of re-mating and residual fertility on the sterile insect technique efficacy: case study with the medfly, Ceratitis capitata. PLoS Comput Biol 20:1\u201335","DOI":"10.1371\/journal.pcbi.1012052"},{"key":"1722_CR32","doi-asserted-by":"crossref","unstructured":"Dumont Y, Duprez M, Privat Y (2025) \u201cSterile insect technique in a patch system: influence of migration rates on optimal single-patch releases strategies,\u201d Journal of Mathematical Biology, vol.\u00a091, no.\u00a071","DOI":"10.1007\/s00285-025-02297-8"},{"issue":"3","key":"1722_CR33","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1006\/tpbi.1994.1032","volume":"46","author":"R Durrett","year":"1994","unstructured":"Durrett R, Levin S (1994) The importance of being discrete (and spatial). Theor Popul Biol 46(3):363\u2013394","journal-title":"Theor Popul Biol"},{"key":"1722_CR34","doi-asserted-by":"publisher","DOI":"10.1201\/9781003035572","volume-title":"Sterile insect technique: principles and practice in area-wide integrated pest management","author":"VA Dyck","year":"2021","unstructured":"Dyck VA, Hendrichs J, Robinson AS (2021) Sterile insect technique: principles and practice in area-wide integrated pest management. Taylor & Francis"},{"issue":"4","key":"1722_CR35","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1079\/BER2006442","volume":"96","author":"S Ekesi","year":"2006","unstructured":"Ekesi S, Nderitu P, Rwomushana I (2006) Field infestation, life history and demographic parameters of the fruit fly Bactrocera invadens (Diptera: Tephritidae) in Africa. Bull Entomol Res 96(4):379\u2013386","journal-title":"Bull Entomol Res"},{"issue":"12","key":"1722_CR36","doi-asserted-by":"publisher","first-page":"6405","DOI":"10.3934\/dcdsb.2021025","volume":"26","author":"B Elbetch","year":"2021","unstructured":"Elbetch B, Benzekri T, Massart D, Sari T (2021) The multi-patch logistic equation. Discrete Contin Dyn Syst Ser B 26(12):6405\u20136424","journal-title":"Discrete Contin Dyn Syst Ser B"},{"key":"1722_CR37","doi-asserted-by":"crossref","unstructured":"Esteva L, Yang HM (2005) Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique. Math Biosci 198(2):132\u2013147","DOI":"10.1016\/j.mbs.2005.06.004"},{"key":"1722_CR38","doi-asserted-by":"crossref","unstructured":"Fauvergue X (2013) A review of mate-finding Allee effects in insects: from individual behavior to population management. Entomol Exp Appl 146(1):79\u201392","DOI":"10.1111\/eea.12021"},{"key":"1722_CR39","doi-asserted-by":"crossref","unstructured":"Grechi I, Preterre A-L, Lardenois M, Ratnadass A (2022) Bactrocera dorsalis invasion increased fruit fly incidence on mango production in Reunion island. Crop Prot 161:106056","DOI":"10.1016\/j.cropro.2022.106056"},{"issue":"12","key":"1722_CR40","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.191090","volume":"6","author":"P Greulich","year":"2019","unstructured":"Greulich P, MacArthur BD, Parigini C, S\u00e1nchez-Garc\u00eda RJ (2019) Stability and steady state of complex cooperative systems: a diakoptic approach. R Soc Open Sci 6(12):191090","journal-title":"R Soc Open Sci"},{"key":"1722_CR41","unstructured":"Hindmarsh AC (1983) \u201cODEPACK, a systematized collection of ODE solvers,\u201d tech. rep., Lawrence Livermore National Laboratory"},{"key":"1722_CR42","volume-title":"Topics in matrix analysis","author":"RA Horn","year":"1994","unstructured":"Horn RA, Johnson CR (1994) Topics in matrix analysis. Cambridge University Press"},{"issue":"1","key":"1722_CR43","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1080\/17513758.2016.1254286","volume":"11","author":"M Huang","year":"2017","unstructured":"Huang M, Song X, Li J (2017) Modelling and analysis of impulsive releases of sterile mosquitoes. J Biol Dyn 11(1):147\u2013171","journal-title":"J Biol Dyn"},{"key":"1722_CR44","unstructured":"Jang E, Dowell R, Manoukis N (2017) \u201cMark-release-recapture experiments on the effectiveness of methyl eugenol\u2013spinosad male annihilation technique against an invading population of Bactrocera dorsalis,\u201d in Proceedings of the Hawaiian Entomological Society, Hawaiian Entomological Society"},{"key":"1722_CR45","doi-asserted-by":"crossref","unstructured":"Ji Q, Chen J, McInnis D, Guo Q (2013) The effect of methyl eugenol exposure on subsequent mating performance of sterile males of Bactrocera dorsalis. J Appl Entomol 137:238\u2013243","DOI":"10.1111\/j.1439-0418.2011.01686.x"},{"issue":"03","key":"1722_CR46","doi-asserted-by":"publisher","first-page":"1450030","DOI":"10.1142\/S1793524514500302","volume":"7","author":"W Jiang","year":"2014","unstructured":"Jiang W, Li X, Zou X (2014) On a reaction-diffusion model for sterile insect release method on a bounded domain. Int J Biomath 7(03):1450030","journal-title":"Int J Biomath"},{"key":"1722_CR47","doi-asserted-by":"publisher","DOI":"10.1201\/b13054","volume-title":"Group inverses of M-matrices and their applications","author":"SJ Kirkland","year":"2012","unstructured":"Kirkland SJ, Neumann M (2012) Group inverses of M-matrices and their applications. CRC Press"},{"issue":"4","key":"1722_CR48","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1093\/jee\/48.4.459","volume":"48","author":"EF Knipling","year":"1955","unstructured":"Knipling EF (1955) Possibilities of insect control or eradication through the use of sexually sterile males. J Econ Entomol 48(4):459\u2013462","journal-title":"J Econ Entomol"},{"issue":"3","key":"1722_CR49","first-page":"237","volume":"15","author":"R Levins","year":"1969","unstructured":"Levins R (1969) Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the ESA 15(3):237\u2013240","journal-title":"Bulletin of the ESA"},{"issue":"2","key":"1722_CR50","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/0025-5564(93)90067-K","volume":"116","author":"M Lewis","year":"1993","unstructured":"Lewis M, Van Den Driessche P (1993) Waves of extinction from sterile insect release. Math Biosci 116(2):221\u2013247","journal-title":"Math Biosci"},{"issue":"1","key":"1722_CR51","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/17513758.2014.977971","volume":"9","author":"J Li","year":"2015","unstructured":"Li J, Yuan Z (2015) Modelling releases of sterile mosquitoes with different strategies. J Biol Dyn 9(1):1\u201314","journal-title":"J Biol Dyn"},{"key":"1722_CR52","doi-asserted-by":"crossref","unstructured":"Li X-L, Zhang J-J, Li D-D, Cai X-Y, Qi Y-X, Lu Y-Y (2024) Toxicity of Beauveria bassiana to Bactrocera dorsalis and effects on its natural predators. Front Microbiol 15:1362089","DOI":"10.3389\/fmicb.2024.1362089"},{"issue":"1","key":"1722_CR53","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/BF00160375","volume":"32","author":"Z Lu","year":"1993","unstructured":"Lu Z, Takeuchi Y (1993) Global asymptotic behavior in single-species discrete diffusion systems. J Math Biol 32(1):67\u201377","journal-title":"J Math Biol"},{"key":"1722_CR54","unstructured":"Markhof FM (1973) \u201cComputer models and application of the sterile-male technique (vienna, 13-17 dec. 1971),\u201d Panel Proceedings Series. INTERNATIONAL ATOMIC ENERGY AGENCY, Vienna, 1973"},{"key":"1722_CR55","doi-asserted-by":"crossref","unstructured":"McCarthy M (1997) The Allee effect, finding mates and theoretical models. Ecol Model 103(1):99\u2013102","DOI":"10.1016\/S0304-3800(97)00104-X"},{"key":"1722_CR56","doi-asserted-by":"crossref","unstructured":"Mutamiswa R, Nyamukondiwa C, Chikowore G, Chidawanyika F (2021) Overview of oriental fruit fly, Bactrocera dorsalis (Hendel)(Diptera: Tephritidae) in Africa: from invasion, bio-ecology to sustainable management. Crop Prot 141:105492","DOI":"10.1016\/j.cropro.2020.105492"},{"key":"1722_CR57","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0024-3795(86)90233-8","volume":"73","author":"R Nussbaum","year":"1986","unstructured":"Nussbaum R (1986) Convexity and log convexity for the spectral radius. Linear Algebra Appl 73:59\u2013122","journal-title":"Linear Algebra Appl"},{"issue":"1","key":"1722_CR58","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1137\/0904010","volume":"4","author":"LR Petzold","year":"1983","unstructured":"Petzold LR (1983) Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J Sci Stat Comput 4(1):136\u2013148","journal-title":"SIAM J Sci Stat Comput"},{"key":"1722_CR59","doi-asserted-by":"crossref","unstructured":"Reinbold-Wasson DD, Reiskind MH (2021) Comparative skip-oviposition behavior among container breeding Aedes spp. mosquitoes (Diptera: Culicidae). J Med Entomol 58(6):2091\u20132100","DOI":"10.1093\/jme\/tjab084"},{"key":"1722_CR60","doi-asserted-by":"crossref","unstructured":"Shelly TE, Edu J (2010) Mark-release-recapture of males of Bactrocera cucurbitae and B. dorsalis (Diptera: Tephritidae) in two residential areas of Honolulu. J Asia-Pac Entomol 13(2):131\u2013137","DOI":"10.1016\/j.aspen.2009.12.003"},{"key":"1722_CR61","doi-asserted-by":"crossref","unstructured":"Singh S, Bajaj K (2022) \u201cMass Trapping of Fruit Flies Using Methyl Eugenol Based Traps,\u201d in Abiotic and Biotic Stress Management in Plants, pp.\u00a0129\u2013153, CRC Press","DOI":"10.1201\/9781003286134-9"},{"key":"1722_CR62","unstructured":"Smith H (1995) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. No.\u00a041, American Mathematical Soc"},{"key":"1722_CR63","doi-asserted-by":"crossref","unstructured":"Stephens PA, Sutherland WJ (1999) Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol Evol 14(10):401\u2013405","DOI":"10.1016\/S0169-5347(99)01684-5"},{"key":"1722_CR64","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1016\/j.apm.2018.11.026","volume":"68","author":"M Strugarek","year":"2019","unstructured":"Strugarek M, Bossin H, Dumont Y (2019) On the use of the sterile insect technique or the incompatible insect technique to reduce or eliminate mosquito populations. Appl Math Model 68:443\u2013470","journal-title":"Appl Math Model"},{"key":"1722_CR65","doi-asserted-by":"crossref","unstructured":"Thom\u00e9 RC, Yang HM, Esteva L (2010) Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide. Math Biosci 223(1):12\u201323","DOI":"10.1016\/j.mbs.2009.08.009"},{"key":"1722_CR66","doi-asserted-by":"crossref","unstructured":"Van den Driessche P (1985) \u201cSome analytical models for biotechnical methods of pest control,\u201d in Pest Control: Operations and Systems Analysis in Fruit Fly Management, pp.\u00a0437\u2013444, Springer","DOI":"10.1007\/978-3-642-70883-1_26"},{"key":"1722_CR67","doi-asserted-by":"crossref","unstructured":"Varga RS (1999) Matrix Oterative Analysis, vol.\u00a027. Springer Science & Business Media","DOI":"10.1007\/978-3-642-05156-2"},{"key":"1722_CR68","doi-asserted-by":"crossref","unstructured":"Vargas RI, Whitehand L, Walsh WA, Spencer JP, Hsu C-L (1995) Aerial releases of sterile Mediterranean fruit fly (Diptera: Tepbritidae) by helicopter: dispersal, recovery, and population suppression. J Econ Entomol 88(5):1279\u20131287","DOI":"10.1093\/jee\/88.5.1279"},{"issue":"4","key":"1722_CR69","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1109\/TAC.1980.1102422","volume":"25","author":"M Vidyasagar","year":"2003","unstructured":"Vidyasagar M (2003) Decomposition techniques for large-scale systems with nonadditive interactions: stability and stabilizability. IEEE Trans Autom Control 25(4):773\u2013779","journal-title":"IEEE Trans Autom Control"},{"issue":"3","key":"1722_CR70","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","volume":"17","author":"P Virtanen","year":"2020","unstructured":"Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, van der Walt SJ, Brett M, Wilson J, Millman KJ, Mayorov N, Nelson ARJ, Jones E, Kern R, Larson E, Carey CJ, Polat \u0130, Feng Y, Moore EW, VanderPlas J, Laxalde D, Perktold J, Cimrman R, Henriksen I, Quintero EA, Harris CR, Archibald AM, Ribeiro AH, Pedregosa F, van Mulbregt P (2020) SciPy 1.0 Contributors, SciPy 1.0: fundamental algorithms for scientific computing in python. Nat Methods 17(3):261\u2013272","journal-title":"Nat Methods"},{"key":"1722_CR71","doi-asserted-by":"crossref","unstructured":"Wee S-L, Rosli NQA (2025) Evaluation of methyl eugenol-supplemented diet as pre-release treatment for simultaneous application of male annihilation and sterile insect techniques against Bactrocera dorsalis. J Pest Sci 98(1):597\u2013606","DOI":"10.1007\/s10340-024-01789-8"},{"issue":"2","key":"1722_CR72","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2019.123660","volume":"483","author":"C Yang","year":"2020","unstructured":"Yang C, Zhang X, Li J (2020) Dynamics of two-patch mosquito population models with sterile mosquitoes. J Math Anal Appl 483(2):123660","journal-title":"J Math Anal Appl"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-026-01722-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11538-026-01722-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-026-01722-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T13:02:07Z","timestamp":1791464527000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11538-026-01722-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,23]]},"references-count":72,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["1722"],"URL":"https:\/\/doi.org\/10.1007\/s11538-026-01722-3","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,23]]},"assertion":[{"value":"7 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"184"}}