Existence and stability of two periodic solutions for an interactive wild and sterile mosquitoes model

References

• S. Ai, J. Li, J. Yu and B. Zheng, Stage-structured models for interactive wild and periodically and impulsively released sterile mosquitoes, Discrete Contin. Dyn. Syst. Ser. B, doi: 10.3934/dcdsb.2021172.
   Google Scholar
• L. Alphey, M. Benedict and R. Bellini, et al. Sterile-insect methods for control of mosquito-borne diseases: An analysis, Vector Borne Zoonotic Dis. 10 (2010), pp. 295–311.
   PubMed Web of Science ®Google Scholar
• H. Barclay, Pest population stability under sterile releases, Res. Popul. Ecol. 24 (1982), pp. 405–416.
   Google Scholar
• H. Barclay, Mathematical models for the use of sterile insects, In: Sterile insect technique: Principles and practice in area-wide integrated pest management, V. Dyck, J. Hendrichs and A. Robinson, eds., Springer, Netherlands, 2005, pp. 147–174.
   Google Scholar
• L. Cai, S. Ai and G. Fan, Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes, Math. Biosci. Eng. 15 (2018), pp. 1181–1202.
   PubMed Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• CDC, Life cycle: The mosquito, Preprint 2019, Available from: https://www.cdc.gov/dengue/resources/factsheets/mosquitolifecyclefinal.pdf.
   Google Scholar
• K. Fister, M. McCarthy, S. Oppenheimer and C. Collins, Optimal control of insects through sterile insect release and habitat modification, Math. Biosci. 244 (2013), pp. 201–212.
   PubMed Web of Science ®Google Scholar
• Z. Guo, H. Guo and Y. Chen, Traveling wavefronts of a delayed temporally discrete reaction-diffusion equation, J. Math. Anal. Appl. 496 (2021), pp. 124787.
   Google Scholar
• M. Hirsch, S. Smale and R. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd ed., Academic Press, Orlando, 2003.
   Google Scholar
• A. Hoffmann, B. Montgomery and J. Popovici, et al. Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission, Nature 476 (2011), pp. 454–457.
   PubMed Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• L. Hu, M. Tang, Z. Wu, Z. Xi and J. Yu, The threshold infection level for wolbachia invasion in random environment, J. Differ. Equ. 266 (2019), pp. 4377–4393.
   Web of Science ®Google Scholar
• 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. Theoret. Biol. 440 (2018), pp. 1–11.
   PubMed Web of Science ®Google Scholar
• M. Huang, M. Tang and J. Yu, Wolbachia infection dynamics by recation-diffusion equations, Sci. China Math 58 (2015), pp. 77–96.
   Web of Science ®Google Scholar
• M. Huang, M. Tang, J. Yu and B. Zheng, A stage structured model of delay differential equations for Aedes mosquito population suppression, Discrete Contin. Dyn. Syst. 40 (2020), pp. 3467–3484.
   Web of Science ®Google Scholar
• M. Huang, J. Yu, L. Hu and B. Zheng, Qualitative analysis for a Wolbachia infection model with diffusion, Sci. China Math. 59 (2016), pp. 1249–1266.
   Web of Science ®Google Scholar
• Y. Hui, G. Lin, J. Yu and J. Li, A delayed differential equation model for mosquito population suppression with sterile mosquitoes, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), pp. 4659–4676.
   Web of Science ®Google Scholar
• I. Iturbe-Ormaetxe, T. Walker and S. O'Neill. Wolbachia and the biological control of mosquito-borne disease, EMBO Rep. 12 (2011), pp. 508–518.
   PubMed Web of Science ®Google Scholar
• J. Li, New revised simple models for interactive wild and sterile mosquito populations and their dynamics, J. Biol. Dyn. 11 (2017), pp. 316–333.
   PubMed Web of Science ®Google Scholar
• G. Lin and Y. Hui, Stability analysis in a mosquito population suppression model, J. Biol. Dyn. 14 (2020), pp. 578–589.
   PubMed Web of Science ®Google Scholar
• Y. Liu, Z. Guo, M. Smaily and L. Wang, A Wolbachia infection model with free boundary, J. Biol. Dyn. 14 (2020), pp. 515–542.
   PubMed Web of Science ®Google Scholar
• Y. Liu, F. Jiao and L. Hu, Modeling mosquito population control by a coupled system, J. Math. Anal. Appl. 506 (2022), pp. 125671.
   Google Scholar
• F. Liu, C. Yao, P. Lin and C. Zhou, Studies on life table of the natural population of Aedes albopictus, Acta Sci. Nat. Univ. Sunyat. 31 (1992), pp. 84–93.
   Google Scholar
• Y. Shi and J. Yu, Wolbachia infection enhancing and decaying domains in mosquito population based on discrete models, J. Biol. Dyn. 14 (2020), pp. 679–695.
   PubMed Web of Science ®Google Scholar
• Y. Shi and B. Zheng, Discrete dynamical models on Wolbachia infection frequency in mosquito populations with biased release ratios, J. Biol. Dyn., 2021, doi: 10.1080/17513758.2021.1977400.
   Google Scholar
• C. Stone, Transient population dynamics of mosquitoes during sterile male releases: Modelling mating behaviour and perturbations of life history parameters, PLoS ONE 8 (2013), pp. e76228. doi: 10.1371/journal.pone.0076228.
   PubMed Web of Science ®Google Scholar
• E. Waltz, US reviews plan to infect mosquitoes with bacteria to stop disease, Nature 533 (2016), pp. 450–451.
   PubMedGoogle Scholar
• S. White, P. Rohani and S. 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.
   Web of Science ®Google Scholar
• World Health Organization, Dengue and severe dengue, Preprint 2021, Available from: http://www.who.int/news-room/fact-sheets/detail/dengue-and-severe-dengue.
   Google Scholar
• J. Yu, Modelling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math. 78 (2018), pp. 3168–3187.
   Web of Science ®Google Scholar
• J. 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.
   Web of Science ®Google Scholar
• J. Yu and J. Li, Dynamics of interactive wild and sterile mosquitoes with time delay, J. Biol. Dyn. 13 (2019), pp. 606–620.
   PubMed Web of Science ®Google Scholar
• J. Yu and J. Li, Global asymptotic stability in an interactive wild and sterile mosquito model, J. Differ. Equ. 269 (2020), pp. 6193–6215.
   Web of Science ®Google Scholar
• J. Yu and B. Zheng, Modeling Wolbachia infection in mosquito population via discrete dynamical models, J. Differ. Equ. Appl. 25 (2019), pp. 1549–1567.
   Web of Science ®Google Scholar
• B. Zheng, J. Li and J. Yu, One discrete dynamical model on Wolbachia infection frequency in mosquito populations, Sci. China Math., (2021), doi: 10.1007/s11425-021-1891-7.
   Google Scholar
• B. Zheng, M. Tang and J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equation, SIAM J. Appl. Math. 74 (2014), pp. 743–770.
   Web of Science ®Google Scholar
• B. Zheng, M. Tang, J. Yu and J. Qiu, Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission, J. Math. Biol. 76 (2018), pp. 235–263.
   PubMed Web of Science ®Google Scholar
• B. Zheng and J. Yu, Characterization of Wolbachia enhancing domain in mosquitoes with imperfect maternal transmission, J. Biol. Dyn. 12 (2018), pp. 596–610.
   PubMed Web of Science ®Google Scholar
• B. Zheng and J. Yu, Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency, Adv. Nonlinear Anal. 11 (2021), pp. 212–224.
   Web of Science ®Google Scholar
• B. Zheng, J. 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 (2021), pp. 718–740.
   Web of Science ®Google Scholar
• X. Zheng, D. Zhang and Y. Li, et al. Incompatible and sterile insect techniques combined eliminate mosquitoes, Nature 572 (2019), pp. 56–61.
   PubMed Web of Science ®Google Scholar
• Z. Zhu, B. Zheng, Y. Shi, R. Yan and J. Yu, Stability and periodicity in a mosquito population suppression model composed of two sub-models, Accepted.
   Google Scholar