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Tianyuan Hengyang Workshop 2020

Uniqueness and stability of periodic solutions for an interactive wild and Wolbachia-infected male mosquito model

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Pages 254-276 | Received 30 Aug 2021, Accepted 26 Jan 2022, Published online: 15 Feb 2022

References

  • F. Baldacchino, B. Caputo, F. Chandre, A. Drago, A. della Torre, F. Montarsi, and A. Rizzoli, Control methods against invasive Aedes mosquitoes in Europe: A review, Pest Manag. Sci. 71 (2015), pp. 1471–1485.
  • S. Boyer, J. Gilles, D. Merancienne, G. Lempérière, and D. Fontenille, Sexual performance of male mosquito Aedes albopictus, Med. Vet. Entomol. 25 (2011), pp. 454–459.
  • O.J. Brady, P.W. Gething, S. Bhatt, J.P. Messina, J.S. Brownstein, A.G. Hoen, C.L. Moyes, A.W.Farlow, T.W. Scott, S.I. Hay, and R. Reithinger, Refining the global spatial limits of dengue virus transmission by evidence-based consensus, Plos Neglect. Trop. D 6(8) (2012), pp. 1–15.
  • J.S. Brownstein, E. Hett, and S.L. O'Neill, The potential of virulent Wolbachia to modulate disease transmission by insects, J. Invertebr. Pathol. 84 (2003), pp. 24–29.
  • L.M. Cai, S. Ai, and J. Li, Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes, SIAM J. Appl. Math. 74(6) (2014), pp. 1786–1809.
  • L.M. Cai, S. Ai, and G. Fan, Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes, Math. Biosci. Eng. 15(5) (2018), pp. 1181–1202.
  • L.M. Cai, J. Huang, X.Y. Song, and Y.Y. Zhang, Bifurcation analysis of a mosquito population model for proportional releasing sterile mosquitoes, Discrete Contin. Dyn. Syst. B 24(11) (2019), pp. 6279–6295.
  • E. Caspari and G.S. Watson, On the evolutionary importance of cytoplasmic sterility in mosquitoes, Evolution 13(4) (1959), pp. 568–570.
  • J. Cohen, Dengue may bring out the worst in Zika, Science 355(6332) (2017), p. 1362.
  • J.E. Crawford, D.W. Clarke, V. Criswell, M. Desnoyer, D. Cornel, B. Deegan, K. Gong, K.C. Hopkins, P. Howell, J.S. Hyde, J. Livni, C. Behling, R. Benza, W. Chen, K.L. Dobson, C. Eldershaw, D. Greeley, Y. Han, B. Hughes, E. Kakani, J. Karbowski, A. Kitchell, E. Lee, T. Lin, J. Liu, M. Lozano, W.MacDonald, J.W. Mains, M. Metlitz, S.N. Mitchell, D. Moore, J.R. Ohm, K. Parkes, A. Porshnikoff, C. Robuck, M. Sheridan, R. Sobecki, P. Smith, J. Stevenson, J. Sullivan, B. Wasson, A.M. Weakley, M. Wilhelm, J. Won, A. Yasunaga, W.C. Chan, J. Holeman, N. Snoad, L. Upson, T. Zha, S.L. Dobson, F.S. Mulligan, P. Massaro, and B.J. White, Efficient production of male Wolbachia-infected Aedes aegypti mosquitoes enables large-scale suppression of wild populations, Nat. Biotechnol. 38 (2020), pp. 482–492.
  • W. Dejnirattisai, P. Supasa, W. Wongwiwat, A. Rouvinski, G. Barba-Spaeth, T. Duangchinda, A.Sakuntabhai, V.-M. Cao-Lormeau, P. Malasit, F.A. Rey, J. Mongkolsapaya, and G.R. Screaton, Dengue virus sero-cross-reactivity drives antibody-dependent enhancement of infection with Zika virus, Nat. Immunol. 17(9) (2016), pp. 1102–1108.
  • C. Dye, Intraspecific competition amongst larval Aedes aegypti: Food exploitation or chemical interference, Ecol. Entomol. 7(1) (1982), pp. 39–46.
  • J.Z. Farkas and P. Hinow, Structured and unstructured continuous models for Wolbachia infections, Bull. Math. Biol. 72 (2010), pp. 2067–2088.
  • 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(2) (2000), pp. 135–140.
  • A.A. Hoffmann, B.L. Montgomery, J. Popovici, I. Iturbe-Ormaetxe, P.H. Johnson, F. Muzzi, M.Greenfield, M. Durkan, Y.S. Leong, 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), pp. 454–457.
  • L. Hu, M. Huang, M. Tang, J. Yu, and B. Zheng, Wolbachia spread dynamics in stochastic environments, Theor. Popul. Biol. 106 (2015), pp. 32–44.
  • L. Hu, M. Tang, Z. Wu, Z. Xi, and J. Yu, The threshold infection level for Wolbachia invasion in random environments, J. Differ. Equ. 266 (2019), pp. 4377–4393.
  • M.G. Huang, M.X. Tang, and J.S. Yu, Wolbachia infection dynamics by reaction-diffusion equations, Sci. China Math. 58(1) (2015), pp. 77–96.
  • A. Jeyaprakash and M.A. Hoy, Long PCR improves Wolbachia DNA amplification: Wsp sequences found in 76% of sixty-three arthropod species, Insect Mol. Biol. 9 (2000), pp. 393–405.
  • M.J. Keeling, F.M. Jiggins, and J.M. Read, The invasion and coexistence of competing Wolbachia strains, Heredity 91 (2003), pp. 382–388.
  • H. Laven, Cytoplasmic inheritance in Culex, Nature 177 (1956), pp. 141–142.
  • J. Li, Simple mathematical models for interacting wild and transgenic mosquito populations, Math. Biosci. 189 (2004), pp. 39–59.
  • J. Li, Differential equations models for interacting wild and transgenic mosquito populations, J. Biol. Dyn. 2(3) (2008), pp. 241–258.
  • J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyn. 11(S2) (2017), pp. 316–333.
  • Y. Li, F. Kamara, G. Zhou, S. Puthiyakunnon, C. Li, Y. Liu, Y. Zhou, L. Yao, G. Yan, X.-G. Chen, and P. Kittayapong, Urbanization increases Aedes albopictus larval habitats and accelerates mosquito development and survivorship, PLoS Negl. Trop. Dis. 8 (2014), p. e3301.
  • G.H. Lin and Y.X. Hui, Stability analysis in a mosquito population suppression model, J. Biol. Dyn. 14(1) (2020), pp. 578–589.
  • F.S. Liu, C.S. Yao, P.Q. Lin, and C.Q. Zhou, Studies on life table of the natural population of Aedes albopictus, Acta Sci. Nat. Univ. Sunyatseni 31(8) (1992), pp. 84–93.
  • Y.F. Liu, F. Jiao, and L.C. Hu, Modeling mosquito population control by a coupled system, J. Math. Anal. Appl. 506 (2022), p. 125671.
  • 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), pp. 141–144.
  • J.L. Rasgon and T.W. Scott, Impact of population age structure on Wolbachia transgene driver efficacy: Ecologically complex factors and release of genetically modified mosquitoes, Insect Biochem. Mol. Biol. 34 (2004), pp. 707–713.
  • P. Schofield, Spatially explicit models of Turelli-Hoffmann Wolbachia invasive wave fronts, J. Theor. Biol. 215 (2002), pp. 121–131.
  • P. Somwang, J. Yanola, W. Suwan, C. Walton, N. Lumjuan, L. Prapanthadara, and P. Somboon, Enzymes-based resistant mechanism in pyrethroid resistant and susceptible Aedes aegypti strains from northern Thailand, Parasitol. Res. 109 (2011), pp. 531–537.
  • M. Turelli, Evolution of incompatibility-inducing microbes and their hosts, Evolution 48(5) (1994), pp. 1500–1513.
  • Y. Wang, X. Liu, C.L. Li, S. Tianyun, J. Jin, Y. Guo, D. Ren, Z. Yang, Q. Liu, and F. Meng, A survey of insecticide resistance in Aedes albopictus (Diptera: Culicidae) during a 2014 dengue fever outbreak in Guangzhou China, J. Econ. Entomol. 110(1) (2017), pp. 239–244.
  • J.H. Werren, D. Windsor, and L. Gao, Distribution of Wolbachia among neotropical arthropods, Proc. R. Soc. Lond. B 262 (1995), pp. 197–204.
  • WHO, Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control, World Health Organization, Geneva, 2009.
  • WHO, Vector-borne diseases, 2 March 2020. Available at https://www.who.int/news-room/fact-sheets/detail/vector-borne-diseases.
  • WHO, Dengue and severe dengue, 19 May 2021. Available at https://www.who.int/news-room/fact-sheets/detail/dengue-and-severe-dengue.
  • Z.Y. Xi, C.C.H. Khoo, and S.L. Dobson, Wolbachia establishment and invasion in an Aedes aegypti laboratory population, Science 310 (2005), pp. 326–328.
  • Z.Y. Xi, C.C.H. Khoo, and S.L. Dobson, Interspecific transfer of Wolbachia into the mosquito disease vector Aedes albopictus, Proc. R. Soc. B 273 (2006), pp. 1317–1322.
  • J.S. Yu, Modelling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math. 78(6) (2018), pp. 3168–3187.
  • J.S. Yu, Existence and stability of a unique and exact two periodic orbits for an interactive wild and sterile mosquito model, J. Differ. Equ. 269 (2020), pp. 10395–10415.
  • J.S. Yu and J. Li, Dynamics of interactive wild and sterile mosquitoes with time delay, J. Biol. Dyn. 13(1) (2019), pp. 606–620.
  • J.S. Yu and J. Li, Global asymptotic stability in an interactive wild and sterile mosquito model, J. Differ. Equ. 269 (2020), pp. 6193–6215.
  • J.S. Yu and B. Zheng, Modelling Wolbachia infection in mosquito population via discrete dynamical models, J. Differ. Equ. Appl. 25(11) (2019), pp. 1549–1567.
  • D. Zhang, X. Zheng, Z. Xi, K. Bourtzis, J.R.L. Gilles, and R. Cordaux, Combining the sterile insect technique with the incompatible insect technique: I-Impact of Wolbachia infection on the fitness of triple-and double-infected strains of Aedes albopictus, PLoS One 10 (2015), p. e0121126.
  • B. Zheng and J.S. Yu, Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency, Adv. Nonlinear Anal. 11 (2022), pp. 212–224.
  • X. Zheng, D. Zhang, Y. Li, C. Yang, Y. Wu, X. Liang, Y. Liang, X. Pan, L. Hu, Q. Sun, X. Wang, Y.Wei, J. Zhu, W. Qian, Z. Yan, A.G. Parker, J.R.L. Gilles, K. Bourtzis, J. Bouyer, M. Tang, B. Zheng, J. Yu, J. Liu, J. Zhuang, Z. Hu, M. Zhang, J.-T. Gong, X.-Y. Hong, Z. Zhang, L. Lin, Q. Liu, Z. Hu, Z. Wu, L.A. Baton, A.A. Hoffmann, and Z. Xi, Incompatible and sterile insect techniques combined eliminate mosquitoes, Nature 572 (2019), pp. 56–61.
  • B. Zheng, J.S. Yu, and J. Li, Modeling and analysis of the implementation of the Wolbachia incompatible and sterile insect technique for mosquito population suppression, SIAM J. Appl. Math. 81(2) (2021), pp. 718–740.
  • B. Zheng, J. Li, and J.S. Yu, One discrete dynamical model on Wolbachia infection frequency in mosquito populations, Sci. China Math. (2022). https://doi.org/10.1007/s11425-021-1891-7.