×

zbMATH — the first resource for mathematics

Miridae control using sex-pheromone traps. Modeling, analysis and simulations. (English) Zbl 1440.37085
Summary: Cocoa mirid, Sahlbergella singularis, is known to be one of the major pests of cocoa in West Africa. In this paper, we consider a biological control method, based on mating disrupting, using artificial sex pheromones, and trapping, to limit the impact of mirids in plots. We develop and study a piece-wise smooth delayed dynamical system. Based on previous results, a theoretical analysis is provided in order to derive all possible dynamics of the system. We show that two main threshold parameters exist that will be useful to derive long term successful control strategies for different level of infestation. We illustrate and discuss our results when cacao pods production is either constant along the year or seasonal. To conclude, we provide future perspectives based on this work.

MSC:
37N25 Dynamical systems in biology
37M05 Simulation of dynamical systems
92D30 Epidemiology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Djoukwe Tapi, M.; Bagny-Beilhe, L.; Bowong, S.; Dumont, Y., Models for miridae, a cocoa insect pest. Application in control strategies, Math. Methods Appl. Sci., 41, 8673-8696 (2018) · Zbl 1406.34031
[2] Mahob, R.; Babin, R.; ten Hoopen, G.; Dibog, L.; Hall, D.; Bilong Bilong, C., Field evaluation of synthetic sex pheromone traps for the cocoa mirid Sahlbergella singularis (Hemiptera: Miridae), Pest Manag. Sci., 67, 6, 672-676 (2011)
[3] Sarfo, J.; Campbell, C.; Hall, D., Optimal pheromone trap density for mass trapping cacao mirids, Entomol. Exp. Appl., 166, 7, 565-573 (2018)
[4] Anguelov, R.; Dufourd, C.; Dumont, Y., Mathematical model for pest-insect control using mating disruption and trapping, Appl. Math. Model., 52, 437-457 (2017) · Zbl 07166336
[5] Joseph, E., Behavioural Responses of Cocoa Mirids, Sahlbergella singularis Hagl. and Distantiella Theobroma Dist. (Heteroptera: Miridae), to Sex Pheromones (2013), University of Greenwich, (Ph.D. thesis)
[6] Dumont, Y.; Tchuenche, J.-M., Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus, J. Math. Biol., 65, 5, 809-855 (2012) · Zbl 1311.92175
[7] Strugarek, M.; Bossin, H.; Dumont, Y., On the use of the sterile insect release technique to reduce or eliminate mosquito populations, Appl. Math. Model., 68, 443-470 (2019)
[8] Bliman, P.; Cardona-Salgado, D.; Dumont, Y.; Vasilieva, O., Implementation of control strategies for sterile insect techniques, Math. Biosci., 314, 43-60 (2019) · Zbl 1425.92126
[9] Hale, J., (Theory of Functional Differential Equations. Theory of Functional Differential Equations, Applied Mathematical Sciences, vol. 3 (1977), Springer: Springer New York) · Zbl 0352.34001
[10] Smith, H., Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems, Ann. Math. Stat., 41 (2008)
[11] Anguelov, R.; Dumont, Y.; Lubuma, J.-S., Mathematical modeling of sterile insect technology for control of anopheles mosquito, Comput. Math. Appl., 64, 3, 374-389 (2012) · Zbl 1252.92044
[12] Smith, H., (An Introduction to Delay Differential Equations with Applications to the Life Sciences. An Introduction to Delay Differential Equations with Applications to the Life Sciences, Texts in Applied Mathematics, vol. 57 (2011), Springer: Springer New York Dordrecht Heidelberg London) · Zbl 1227.34001
[13] Anguelov, R.; Dufourd, C.; Dumont, Y., Simulations and parameter estimation of a trap-insect model using a finite element approach, Math. Comput. Simulation, 133, 47-75 (2017)
[14] Barton, D., Stability calculations for piecewise-smooth delay equations, Int. J. Bifurcation Chaos, 19, 639-650 (2009) · Zbl 1170.34350
[15] Bernardo, M.; Budd, C.; Champneys, A.; Kowalczyk, P., Piecewise-Smooth Dynamical Systems: Theory and Applications, Vol. 163 (2008), Springer Science & Business Media · Zbl 1146.37003
[16] Bisselua, D.; Yede, C.; Vidal, S., Dispersion models and sampling of cacao mirid bug Sahlbergella singularis (Hemiptera: Miridae) on Theobroma cacao in Southern Cameroon, Environ. Entomol., 40, 1, 111-119 (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.