Citation: Liming Cai, Shangbing Ai, Guihong Fan. Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1181-1202. doi: 10.3934/mbe.2018054
[1] | [ R. Abdul-Ghani,H. F. Farag,A. F. Allam,A. A. Azazy, Measuring resistant-genotype transmission of malaria parasites: challenges and prospects, Parasitol Res., 113 (2014): 1481-1487. |
[2] | [ P. L. Alonso, G. Brown, M. Arevalo-Herrera, et al, A research agenda to underpin malaria eradication, PLoS Med., 8 (2011), e1000406. |
[3] | [ L. Alphey,M. Benedict,R. Bellini,G. G. Clark,D. A. Dame,M. W. Service,S. L. Dobson, Sterile-insect methods for control of mosquito-borne diseases: An analysis, Vector Borne Zoonotic Dis., 10 (2010): 295-311. |
[4] | [ J. Arino,L. Wang,G. S. Wolkowicz, An alternative formulation for a delayed logistic equation, J. Theor. Biol., 241 (2006): 109-119. |
[5] | [ M. Q. Benedict,A. S. Robinson, The first releases of transgenic mosquitoes: An argument for the sterile insect technique, Trends Parasitol, 19 (2003): 349-355. |
[6] | [ E. Beretta,Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002): 1144-1165. |
[7] | [ J. G. Breman, The ears of the hippopotamus: Manifestations, determinants, and estimates of the malaria burden, Am. J. Trop. Med. Hyg., 64 (2001): 1-11. |
[8] | [ W. G. Brogdon,J. C. McAllister, Insecticide resistance and vector control, J. Agromedicine, 6 (1999): 41-58. |
[9] | [ L. Cai,S. Ai,J. Li, Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes, SIAM, J. Appl. Math., 74 (2014): 1786-1809. |
[10] | [ K. Cooke,P. van den Driessche,X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 39 (1999): 332-352. |
[11] | [ H. Diaz,A. A. Ramirez,A. Olarte,C. Clavijo, A model for the control of malaria using genetically modified vectors, J. Theor. Biol., 276 (2011): 57-66. |
[12] | [ J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1960. |
[13] | [ Y. Dumont,J. M. Tchuenche, Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus, J. Math. Biol., 65 (2012): 809-854. |
[14] | [ V. A. Dyck, J. Hendrichs and A. S. Robinson, Sterile insect technique -principles and practice in area-wide integrated pest management, Springer, The Netherlands, 2005. |
[15] | [ C. Dye, Models for the population dynamics of the yellow fever mosquito, Aedes aegypti, J. Anim. Ecol., 53 (1984): 247-268. |
[16] | [ L. Esteva,H. M. Yang, Assessing the effects of temperature and dengue virus load on dengue transmission, J. Biol. Syst., 23 (2015): 527-554. |
[17] | [ L. Esteva,H. M. Yang, Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique, Math. Biosci., 198 (2005): 132-147. |
[18] | [ J. E. Gentile,S. Rund,G. R Madey, Modelling sterile insect technique to control the population of Anopheles gambiae, Malaria J., 14 (2015): 92-103. |
[19] | [ J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equation, Springer, New York, 1993. |
[20] | [ J. Ito,A. Ghosh,L. A. Moreira,E. A. Wilmmer,M. Jacobs-Lorena, Transgenic anopheline mosquitoes impaired in transmission of a malria parasite, Nature, 417 (2002): 452-455. |
[21] | [ M. Jankovic,S. Petrovskii, Are time delays always destabilizing? Revisiting the role of time delays and the Allee effect, Theor Ecol., 7 (2014): 335-349. |
[22] | [ E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males, J. Econ. Entomol., 48 (1955): 459-462. |
[23] | [ Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993. |
[24] | [ S. S. Lee,R. E. Baker,E. A. Gaffney,S. M. White, Modelling Aedes aegypti mosquito control via transgenic and sterile insect techniques: Endemics and emerging outbreaks, J. Theor. Biol., 331 (2013): 78-90. |
[25] | [ M. A. Lewis,P. van den Driessche, Waves of extinction from sterile insect release, Math. Biosci., 116 (1993): 221-247. |
[26] | [ J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyna., 11 (2017): 316-333. |
[27] | [ J. Li,L. Cai,Y. Li, Stage-structured wild and sterile mosquito population models and their dynamics, J. Biol.Dyna., 11 (2017): 79-101. |
[28] | [ J. Lu,J. Li, Dynamics of stage-structured discrete mosquito population, J. Appl. Anal. Comput., 1 (2011): 53-67. |
[29] | [ G. J. Lycett,F. C. Kafatos, Anti-malaria mosquitoes?, Nautre, 417 (2002): 387-388. |
[30] | [ C. W. Morin,A. C. Comrie, Regional and seasonal response of a West Nile virus vector to climate change, PNAS, 110 (2013): 15620-15625. |
[31] | [ W. W. Murdoch, C. J. Briggs and R. M. Nisbet, Consumer-resource dynamics, Princeton University Press, New Jersey, USA, 2003. |
[32] | [ H. K. Phuc, M. H. Andreasen, et al, Late-acting dominant lethal genetic systems and mosquito control, BMC. Biol., 5 (2007), 11–16. |
[33] | [ E. P. Pliego,J. Vel$\acute{a}$zquez-Castro,A. F. Collar, Seasonality on the life cycle of Aedes aegypti mosquito and its statistical relation with dengue outbreaks, Appl. Math. Model., 50 (2017): 484-496. |
[34] | [ M. Rafikov,L. Bevilacqua,A. P. Wyse, Optimal control strategy of malaria vector using genetically modified mosquitoes, J. Theor. Biol., 258 (2009): 418-425. |
[35] | [ S. J. Schreiber, Allee effect, extinctions, and chaotic transients in simple population models, Theor. Popul. Biol., 64 (2003): 201-209. |
[36] | [ J. Smith,M. Amador,R. Barrera, Seasonal and habitat effects on dengue and West Nile Virus Vectors in San Juan, Puerto Rico, J. Am. Mosq. Control. Assoc., 25 (2009): 38-46. |
[37] | [ H. Townson, SIT for African malaria vectors: Epilogue, Malar. J., 8 (2009), S10. |
[38] | [ WHO, 10 facts on malaria, http://www.who.int/features/factfiles/malaria/en/. |
[39] | [ J. Wu,H. R. Thieme,Y. Lou,G. Fan, Stability and persistence in ODE models for populations with many stages, Math. Biosc. Eng., 12 (2015): 661-686. |
[40] | [ B. Zheng,M. Tang,J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equations, SIAM J. Appl. Math., 74 (2014): 743-770. |
[41] | [ B. Zheng,M. Tang,J. Yu,J. Qiu, Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission, J. Math. Biol., 76 (2018): 235-263. |