Ecology and evolution
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Ecology and evolution
Article Number 76
Number of page(s) 26
DOI https://doi.org/10.1051/mmnp/2020041
Published online 15 December 2020
  1. T.H. Ant, C.S. Herd, V. Geoghegan, A.A. Hoffmann and S.P. Sinkins, The wolbachia strain wau provides highly efficient virus transmission blocking in aedes aegypti. PLoS Pathogens 14 (2018) e1006815. [CrossRef] [PubMed] [Google Scholar]
  2. Z.A. Awrahman, F. Champion de Crespigny and N. Wedell, The impact of wolbachia, male age and mating history on cytoplasmic incompatibility and sperm transfer in drosophila simulans. J. Evolut. Biol. 27 (2014) 1–10. [CrossRef] [Google Scholar]
  3. J.K. Axford, P.A. Ross, H.L. Yeap, A.G. Callahan and A.A. Hoffmann, Fitness of walbb wolbachia infection in aedes aegypti: parameter estimates in an outcrossed background and potential for population invasion. Am. J. Trop. Med. Hygiene 94 (2016) 507–516. [CrossRef] [Google Scholar]
  4. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 33 (2002) 1144–1165. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Berezansky, E. Braverman and L. Idels, Nicholson’s blowflies differential equations revisited: Main results and open problems. Appl. Math. Model. 34 (2010) 1405–1417. [CrossRef] [Google Scholar]
  6. L. Berezansky, L. Idels and L. Troib, Global dynamics of nicholson-type delay systems with applications. Nonlinear Anal.: Real World Appl. 12 (2011) 436–445. [CrossRef] [Google Scholar]
  7. P.-A. Bliman, M.S. Aronna, F.C. Coelho and M.A. H.B. da Silva, Ensuring successful introduction of wolbachia in natural populations of aedes aegypti by means of feedback control. J. Math. Biol. 76 (2018) 1269–1300. [CrossRef] [PubMed] [Google Scholar]
  8. P.-A. Bliman, D. Cardona-Salgado, Y. Dumont and O. Vasilieva, Implementation of control strategies for sterile insect techniques. Math. Biosci. 314 (2019) 43–60. [CrossRef] [Google Scholar]
  9. S.R. Bordenstein and S.R. Bordenstein, Temperature affects the tripartite interactions between bacteriophage wo, wolbachia, and cytoplasmic incompatibility. PLoS ONE 6 (2011) e29106. [CrossRef] [Google Scholar]
  10. E. Braverman and D. Kinzebulatov, Nicholson’s blowflies equation with a distributed delay. Can. Appl. Math. Quart. 14 (2006) 107–128. [Google Scholar]
  11. R.A. Costello, Effects of environmental and physiological factors on the acoustic behavior of Aedes aegypti (L.) (Diptera: Culicidae). PhD thesis, University of Manitoba, Canada (1974). [Google Scholar]
  12. C. Dye, Models for the population dynamics of the yellow fever mosquito, Aedes aegypti. J. Animal Ecol. 53 (1984) 247–268. [CrossRef] [Google Scholar]
  13. J.Z. Farkas and P. Hinow, Structured and unstructured continuous models for wolbachia infections. Bull. Math. Biol. 72 (2010) 2067–2088. [CrossRef] [Google Scholar]
  14. J.Z. Farkas, S.A. Gourley, R. Liu and A.A. Yakubu, Modelling wolbachia infection in a sex-structured mosquito population carrying west nile virus. J. Math. Biol. 75 (2017). [CrossRef] [PubMed] [Google Scholar]
  15. C.P. Ferreira, Aedes aegypti and wolbachia interaction: population persistence in a changing environment. Theor. Ecol. (2019). [Google Scholar]
  16. C.P. Ferreira, H.M. Yang and L. Esteva, Assessing the suitability of sterile insect technique applied to Aedes aegypti. J. Biol. Syst. 16 (2008) 565–577. [CrossRef] [Google Scholar]
  17. D.J. Gubler, The global emergence/resurgence of arboviral diseases as public health problems. Arch. Med. Res. 33 (2002) 330–342. [CrossRef] [PubMed] [Google Scholar]
  18. N.D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation. J. London Math. Soc. (1950) 226–232. [CrossRef] [MathSciNet] [Google Scholar]
  19. S.P. Hernandez, A.M. Loaiza and C.A.A. Minoli, A reaction-diffusion model for controlling the Aedes aegypti with wolbachia. Int. J. Contemp. Math. Sci. 11 (2016) 385–394. [CrossRef] [Google Scholar]
  20. A.A. Hoffmann, B.L. Montgomery, J. Popovici, I. Iturbe-Ormaetxe, P.H. Johnson, F. Muzzi, M. Greenfield, M. Durkan, Y.S. Leonga, Y. Dong, H. Cook, J. Axford, A.G. Callahan, N. Kenny, C. Omodei, E.A. McGraw, P.A. Ryan, S.A. Ritchie, M. Turelli and S.L. O’Neill, Successful establishment of wolbachia in aedes populations to suppress dengue transmission. Nature 476 (2011) 454–457. [CrossRef] [PubMed] [Google Scholar]
  21. M. Huang, M.X. Tang and J.S. Yu, Wolbachia infection dynamics by reaction-diffusion equations. Sci. China Math. 58 (2015) 77–96. [CrossRef] [Google Scholar]
  22. M. Huang, J. Luo, L. Hu, B. Zheng and J. Yu, Assessing the efficiency of wolbachia driven aedes mosquito suppression by delay differential equations. J. Theor. Biol. 440 (2018). [CrossRef] [PubMed] [Google Scholar]
  23. M.G. Huang, M.X. Tang, J.S. Yu and B. Zheng, The impact of mating competitiveness and incomplete cytoplasmic incompatibility on wolbachia-driven mosquito population suppression. Math. Biosci. Eng. 16 (2019) 4741–4757. [CrossRef] [PubMed] [Google Scholar]
  24. H. Hughes and N. Britton, Modelling the use of wolbachia to control dengue fever transmission. Bull. Math. Biol. 75 (2013). [CrossRef] [Google Scholar]
  25. L. Idels and M Kipnis, Stability criteria for a nonlinear nonautonomous system with delays. Appl. Math. Model. 33 (2009) 2293–2297. [CrossRef] [Google Scholar]
  26. S. Lunel and J. Hale, Introduction to functional differential equations. In Vol. 99 of Applied Mathematical Sciences. Springer-Verlag (1993). [Google Scholar]
  27. M. Keeling, F.M. Jiggins and J.M. Read, The invasion and coexistence of competing wolbachia strains. Heredity 91 (2003) 382–388. [CrossRef] [PubMed] [Google Scholar]
  28. J.G. King, C. Souto-Maior, L.M. Sartori, R.M. de Freitas and M. Gomes, Variation in wolbachia effects on aedes mosquitoes as a determinant of invasiveness and vectorial capacity. Nat. Commun. 9 (2018). [Google Scholar]
  29. X. Ling, A.M. Carrie, T. Panpim and M.H. James, Two-sex mosquito model for the persistence of wolbachia. J. Biol. Dyn. 11 (2017) 216–237. [CrossRef] [PubMed] [Google Scholar]
  30. C.J. McMeniman, R.V. Lane, B.N. Cass, A.W.C. Fong, M. Sidhu, Y.-F. Wang and S.L. O’Neill, Stable introduction of a life-shortening wolbachia infection into the mosquito Aedes aegypti. Science 323 (2009) 141–144. [CrossRef] [PubMed] [Google Scholar]
  31. M. Ndii, R. Hickson and G. Mercer, Modelling the introduction of wolbachia into Aedes aegypti mosquitoes to reduce dengue transmission. ANZIAM J. 53 (2012) 213–227. [Google Scholar]
  32. Z. Qu, L. Xue and J. Hyman, Modeling the transmission of wolbachia in mosquitoes for controlling mosquito-borne diseases. SIAM J. Appl. Math. 78 (2018) 826–852. [CrossRef] [Google Scholar]
  33. M. Rafikov, E. Rafikova and H.M. Yang, Optimization of the Aedes aegypti control strategies for integrated vector management. J. Appl. Math. 2015 (2015) 918194. [CrossRef] [Google Scholar]
  34. J.M. Reinhold, C.R. Lazzari and C. Lahondère, Effects of the environmental temperature on Aedes aegypti and Aedes albopictus mosquitoes: a review. Insects 9 (2018) 158. [CrossRef] [Google Scholar]
  35. P.A. Ross, I. Wiwatanaratanabutr, J.K. Axford, V.L. White, N.M. Endersby-Harshman and A.A. Hoffmann, Wolbachia infections in aedes aegypti differ markedly in their response to cyclical heatstress (2017). [Google Scholar]
  36. I.E. Leonard T. Hillen and H. Van Roessel Partial Differential Equations: Theory and Completely Solved Problems. Wiley (2012). [Google Scholar]
  37. Z. Veneti, M.E. Clark, T.L. Karr, C. Savakis and K. Bourtzis, Heads or tails: Host-parasite interactions in the drosophila-wolbachia system. Appl. Environ. Microbiol. 70 (2004) 5366–5372. [CrossRef] [Google Scholar]
  38. P.F. Viana-Medeiros, D.F. Bellinato, A.J. Martins and D. Valle, Insecticide resistance, associated mechanisms and fitness aspects in two Brazilian Stegomyia aegypti (= Aedes aegypti) populations. Med. Veterin. Entomol. 31 (2017) 340–350. [CrossRef] [Google Scholar]
  39. T. Walker, P.H. Johnson, L.A. Moreira, I. Iturbe-Ormaetxe, F.D. Frentiu, C.J. McMeniman, Y.S. Leong, Y. Dong, J. Axford, P. Kriesner, A.L. Lloyd, S.A. Ritchie, S.L. O’Neill and A.A. Hoffmann, The WMEL wolbachia strain blocks dengue and invades caged Aedes aegypti populations. Nature 475 (2011) 450–453. [CrossRef] [Google Scholar]
  40. Z. Xi, C.C. Khoo and S.L. Dobson, Wolbachia establishment and invasion in an Aedes aegypti laboratory population. Science 310 (2005) 326–328. [CrossRef] [Google Scholar]
  41. H.M. Yang and C.P. Ferreira, Assessing the effects of vector control on dengue transmission. Appl. Math. Comput. 198 (2008) 401–413. [Google Scholar]
  42. H.M. Yang, M.L. Macoris, K.C. Galvani, M.T. Andrighetti and D.M. Wanderley, Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue. Epidemiol. Infection 137 (2009) 1188–1202. [CrossRef] [Google Scholar]
  43. H.L. Yeap, P. Mee, T. Walker, A.R. Weeks, S.L. O’Neill, P. Johnson, S.A. Ritchie, K.M. Richardson, C. Noteg, N.M. Endersby and A.A. Hoffmann, Dynamics of the ‘popcorn’ wolbachia infection in outbred Aedes aegypti informs prospects for mosquito vector control. Genetics 187 (2011) 583–595. [CrossRef] [PubMed] [Google Scholar]

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