zbMATH — the first resource for mathematics

New revised simple models for interactive wild and sterile mosquito populations and their dynamics. (English) Zbl 1448.92217
Summary: Based on previous research, we formulate revised, new, simple models for interactive wild and sterile mosquitoes which are better approximations to real biological situations but mathematically more tractable. We give basic investigations of the dynamical features of these simple models such as the existence of equilibria and their stability. Numerical examples to demonstrate our findings and brief discussions are also provided.

92D25 Population dynamics (general)
34D23 Global stability of solutions to ordinary differential equations
Full Text: DOI
[1] L. Alphey, M. Benedict, R. Bellini, G.G. Clark, D.A. Dame, M.W. Service, and S.L. Dobson, Sterile-insect methods for control of mosquito-borne diseases: An analysis, Vector Borne Zoonotic Dis. 10 (2010), pp. 295-311. doi: 10.1089/vbz.2009.0014[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[2] H.J. Barclay, The sterile insect release method on species with two-stage life cycles, Res. Popul. Ecol. 21 (1980), pp. 165-180. doi: 10.1007/BF02513619[Crossref], [Google Scholar]
[3] H.J. Barclay, Pest population stability under sterile releases, Res. Popul. Ecol. 24 (1982), pp. 405-416. doi: 10.1007/BF02515585[Crossref], [Google Scholar]
[4] H.J. Barclay, Modeling incomplete sterility in a sterile release program: Interactions with other factors, Popul. Ecol. 43 (2001), pp. 197-206. doi: 10.1007/s10144-001-8183-7[Crossref], [Web of Science ®], [Google Scholar]
[5] H.J. Barclay, Mathematical models for the use of sterile insects, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management, V.A. Dyck, J. Hendrichs, and A.S. Robinson eds., Springer, Heidelberg, 2005, pp. 147-174. [Google Scholar]
[6] H.J. Barclay and M. Mackauer, The sterile insect release method for pest control: A density dependent model, Environ. Entomol. 9 (1980), pp. 810-817. doi: 10.1093/ee/9.6.810[Crossref], [Web of Science ®], [Google Scholar]
[7] A.C. Bartlett and R.T. Staten, Sterile Insect Release Method and other Genetic Control Strategies, Radcliffe’s IPM World Textbook, 1996. Available at https://protect-us.mimecast.com/s/zNXlBdUbR4D5cD?domain=ipmworld.umn.edu. [Google Scholar]
[8] N. Becker, Mosquitoes and Their Control, Kluwer Academic/Plenum, New York, 2003. [Crossref], [Google Scholar]
[9] L. Cai, S. Ai, and J. Li, Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes, SIAM J. Appl. Math. 74 (2014), pp. 1786-1809. doi: 10.1137/13094102X[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1320.34071
[10] C. Dye, Intraspecific competition amongst larval Aedes aegypti: Food exploitation or chemical interference, Ecol. Entomol. 7 (1982), pp. 39-46. doi: 10.1111/j.1365-2311.1982.tb00642.x[Crossref], [Web of Science ®], [Google Scholar]
[11] K.R. Fister, M.L. McCarthy, S.F. Oppenheimer, and C. Collins, Optimal control of insects through sterile insect release and habitat modification, Math. Biosci. 244 (2013), pp. 201-212. doi: 10.1016/j.mbs.2013.05.008[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1280.92025
[12] J.C. Flores, A mathematical model for wild and sterile species in competition: Immigration, Phys. A 328 (2003), pp. 214-224. doi: 10.1016/S0378-4371(03)00545-4[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1026.92051
[13] R.M. Gleiser, J. Urrutia, and D.E. Gorla, Effects of crowding on populations of Aedes albifasciatus larvae under laboratory conditions, Entomol. Exp. Appl. 95 (2000), pp. 135-140. doi: 10.1046/j.1570-7458.2000.00651.x[Crossref], [Web of Science ®], [Google Scholar]
[14] J. Li, Malaria model with stage-structured mosquitoes, Math. Biol. Eng. 8 (2011), pp. 753-768. doi: 10.3934/mbe.2011.8.753[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1260.92060
[15] J. Li, Modeling of transgenic mosquitoes and impact on malaria transmission, J. Biol. Dynam. 5 (2011), pp. 474-494. doi: 10.1080/17513758.2010.523122[Taylor & Francis Online], [Google Scholar] · Zbl 1225.92033
[16] J. Li and Z. Yuan, Modeling releases of sterile mosquitoes with different strategies, J. Biol. Dynam. 9 (2015), pp. 1-14. doi: 10.1080/17513758.2014.977971[Taylor & Francis Online], [Google Scholar]
[17] J. Li, L. Cai, and Y. Li, Stage-structured wild and sterile mosquito population models and their dynamics, J. Biol. Dynam. (2016). Available at https://protect-us.mimecast.com/s/rx4mBRUMbaWRTa?domain=dx.doi.org. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[18] M. Otero, H.G. Solari, and N. Schweigmann, A stochastic population dynamics model for Aedes aegypti: Formulation and application to a city with temperate climate, Bull. Math. Biol. 68 (2006), pp. 1945-1974. doi: 10.1007/s11538-006-9067-y[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1296.92215
[19] C.M. Stone, Transient population dynamics of mosquitoes during sterile male releases: Modelling mating behaviour and perturbations of life history parameters, PLoS ONE 8 (2013), p. e76228. doi: 10.1371/journal.pone.0076228[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[20] S.M. White, P. Rohani, and S.M. Sait, Modelling pulsed releases for sterile insect techniques: Fitness costs of sterile and transgenic males and the effects on mosquito dynamics, J. Appl. Ecol. 47 (2010), pp. 1329-1339. doi: 10.1111/j.1365-2664.2010.01880.x[Crossref], [Web of Science ®], [Google Scholar]
[21] Wikipedia, Sterile insect technique, 2014. Available at https://protect-us.mimecast.com/s/ZpWJBRu1q48kTn?domain=en.wikipedia.org. [Google Scholar]
[22] L. Yakob, L. Alphey, and M.B. Bonsall, Aedes aegypti control: The concomitant role of competition, space and transgenic technologies, J. Appl. Ecol. 45 (2008), pp. 1258-1265. doi: 10.1111/j.1365-2664.2008.01498.x[Crossref], [Web of Science ®], [Google Scholar]
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.