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On the use of the sterile insect release technique to reduce or eliminate mosquito populations. (English) Zbl 07183476
Summary: Vector control is critical to limit the circulation of vector-borne diseases, like chikungunya, dengue or zika, which have become important issues around the world. Among them, the Sterile Insect Technique (SIT) and the Incompatible Insect Technique (IIT) have recently aroused a renewed interest. In this paper we derive and study a minimalistic mathematical model designed for Aedes mosquito population elimination by SIT/IIT. Contrary to most of the previous models, it is bistable in general, allowing simultaneously for elimination of the population and for its survival. We consider different types of releases (constant, periodic or impulsive) and show necessary conditions to reach elimination in each case. We also estimate both sufficient and minimal treatment times. Biological parameters are estimated from a case study of an Aedes polynesiensis population, for which extensive numerical investigations illustrate the analytical results. The applications of this work are two-fold: to help identifying some key parameters that may need further field investigations, and to help designing release protocols.

MSC:
92 Biology and other natural sciences
37 Dynamical systems and ergodic theory
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[1] Anguelov, R.; Dumont, Y.; Lubuma, J., Mathematical modeling of sterile insect technology for control of anopheles mosquito, Comput. Math. Appl., 64, 3, 374-389 (2012) · Zbl 1252.92044
[2] Anguelov, R.; Dumont, Y.; Lubuma, J., On nonstandard finite difference schemes in biosciences, AIP Conf. Proc., 1487, 212-223 (2012)
[3] Bainov, D.; Simeonov, P., Impulsive Differential Equations: Periodic Solutions and Applications, 66 (1993), CRC Press · Zbl 0815.34001
[4] Bliman, P.-A.; Aronna, M. S.; Coelho, F. C.; da Silva, M. A.H. B., Ensuring successful introduction of wolbachia in natural populations of Aedes aegypti by means of feedback control, J. Math. Biol., 76, 5, 1269-1300 (2018) · Zbl 1392.92096
[5] Bourtzis, K., Wolbachia- based technologies for insect pest population control, Advances in Experimental Medicine and Biology, 627 (2008), Springer, New York, NY
[6] Chambers, E.; Hapairai, L. K.M.; Peel, B. A.; Bossin, H.; Dobson, S., Male mating competitiveness of a Wolbachia-introgressed Aedes polynesiensis strain under semi-field conditions, PLoS Negl. Trop. Dis., 5, e1271 (2011)
[7] Dufourd, C.; Dumont, Y., Modeling and simulations of mosquito dispersal. the case of Aedes albopictus, Biomath, 1209262, 1-7 (2012) · Zbl 1368.92141
[8] Dufourd, C.; Dumont, Y., Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control, Comput. Math. Appl., 66, 9, 1695-1715 (2013) · Zbl 1345.34105
[9] 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
[10] Dumont, Y.; Thuilliez, J., Human behaviors: A threat to mosquito control?, Math. Biosci., 281, Supplement C, 9-23 (2016) · Zbl 1352.92149
[11] Durrett, R.; Levin, S. A., The importance of being discrete (and spatial), Theor. Popul. Biol., 46, 363-394 (1994) · Zbl 0846.92027
[12] Dyck, V. A.; Hendrichs, J.; Robinson, A. S., The Sterile Insect Technique, Principles and Practice in Area-Wide Integrated Pest Management (2006), Springer, Dordrecht
[13] Farkas, J. Z.; Gourley, S. A.; Liu, R.; Yakubu, A.-A., Modelling Wolbachia infection in a sex-structured mosquito population carrying west nile virus, J. Math. Biol., 75, 3, 621-647 (2017) · Zbl 1387.92082
[14] Farkas, J. Z.; Hinow, P., Structured and unstructured continuous models for Wolbachia infections, Bull. Math. Biol., 72, 8, 2067-2088 (2010) · Zbl 1201.92044
[15] 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 Nat., 178, 333-342 (2011)
[16] Hapairai, L. K.M., Studies on Aedes polynesiensis introgression and ecology to facilitate lymphatic filariasis control (2013), University of Oxford, Ph.D. thesis
[17] Hapairai, L. K.M.; Marie, J.; Sinkins, S. P.; Bossin, H., Effect of temperature and larval density on Aedes polynesiensis (diptera: Culicidae) laboratory rearing productivity and male characteristics, Acta tropica, 132 (2013)
[18] Hapairai, L. K.M.; Sang, M. A.C.; Sinkins, S. P.; Bossin, H. C., Population studies of the filarial vector Aedes polynesiensis (diptera: Culicidae) in two island settings of french polynesia, J. Med. Entomol., 50, 5, 965-976 (2013)
[19] Hertig, M.; Wolbach, S. B., Studies on Rickettsia-like micro-organisms in insects, J. Med. Res., 44, 3, 329 (1924)
[20] Huang, M.; Song, X.; Li, J., Modelling and analysis of impulsive releases of sterile mosquitoes, J. Biol. Dyn., 11, 1, 147-171 (2017)
[21] Hughes, H.; Britton, N. F., Modeling the Use of Wolbachia to Control Dengue Fever Transmission., Bull. Math. Biol., 75, 796-818 (2013) · Zbl 1273.92034
[22] Jachowski Jr., L., Filariasis in american samoa. y. bionomics of the principal vector, Aedes polynesiensis marks., Am. J. Hyg., 60, 2, 186-203 (1954)
[23] Lees, R.; Knols, B.; Bellini, R.; Benedict, M.; Bheecarry, A.; Bossin, H.; Chadee, D.; Charlwood, J.; Dabiré, R.; Djogbenou, L.; Egyir-Yawson, A.; Gato, R.; Gouagna, L.; Hassan, M.; Khan, S.; Koekemoer, L.; Lemperiere, G.; C Manoukis, N.; Mozuraitis, R.; Gilles, J., Review: Improving our knowledge of male mosquito biology in relation to genetic control programmes, Acta tropica, 132S, S2-S11 (2014)
[24] Li, J.; Yuan, Z., Modelling releases of sterile mosquitoes with different strategies, J. Biol. Dyn., 9, 1, 1-14 (2015)
[25] Moreira, L. A.; Iturbe-Ormaetxe, I.; Jeffery, J. A.; Lu, G.; Pyke, A. T.; Hedges, L. M.; Rocha, B. C.; Hall-Mendelin, S.; Day, A.; Riegler, M.; Hugo, L. E.; Johnson, K. N.; Kay, B. H.; McGraw, E. A.; van den Hurk, A. F.; Ryan, P. A.; O’Neill, S. L., A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell, 139, 7, 1268-1278 (2009)
[26] Nadin, G.; Strugarek, M.; Vauchelet, N., Hindrances to bistable front propagation: application to Wolbachia invasion, J. Math. Biol., 76, 6, 1489-1533 (2018) · Zbl 1411.34039
[27] O’Connor, L.; Plichart, C.; Sang, A. C.; Brelsfoard, C. L.; Bossin, H. C.; Dobson, S. L., Open release of male mosquitoes infected with a Wolbachia biopesticide: Field performance and infection containment, PLOS Negl. Trop. Dis., 6, 11, 1-7 (2012)
[28] Oliva, C. F.; Damiens, D.; Benedict, M. Q., Male reproductive biology of Aedes mosquitoes, Acta Tropica, 132, Supplement, S12-S19 (2014)
[29] Oliva, C. F.; Jacquet, M.; Gilles, J.; Lemperiere, G.; Maquart, P.-O.; Quilici, S.; Schooneman, F.; Vreysen, M. J.B.; Boyer, S., The sterile insect technique for controlling populations of Aedes albopictus (diptera: Culicidae) on reunion island: Mating vigour of sterilized males, PLOS ONE, 7, 11, 1-8 (2012)
[30] 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)
[31] Rivière, F., Ecologie de Aedes (Stegomyia) polynesiensis, Marks, 1951, et transmission de la filariose de Bancroft en Polynésie (1988), ORSTOM, Ph.D. thesis
[32] Sallet, G.; da Silva, M. A.H. B., Monotone dynamical systems and some models of Wolbachia in Aedes aegypti populations, ARIMA, 20, 145-176 (2015)
[33] Schraiber, J. G.; Kaczmarczyk, A. N.; Kwok, R.; Park, M.; Silverstein, R.; Rutaganira, F. U.; Aggarwal, T.; Schwemmer, M. A.; Hom, C. L.; Grosberg, R. K.; Schreiber, S. J., Constraints on the use of lifespan-shortening Wolbachia to control dengue fever, J. Theor. Biol., 297, 26-32 (2012) · Zbl 1336.92085
[34] Sinkins, S. P., Wolbachia and cytoplasmic incompatibility in mosquitoes, Insect Biochem. Mol. Biol., 34, 7, 723-729 (2004)
[35] Smith, H. L., Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. (1995), Providence, R.I.: Am. Math. Soc. · Zbl 0821.34003
[36] Strugarek, M.; Vauchelet, N.; Zubelli, J., Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model, Math. Biosci. Eng., 15(4), 961-991 (2018) · Zbl 1406.92522
[37] Suzuki, T.; Sone, F., Breeding habits of vector mosquitoes of filariasis and dengue fever in western samoa, Med. Entomol. Zool., 29, 279-286 (1978)
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