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Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model

Author

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  • Lijie Chang

    (Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
    College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China)

  • Yantao Shi

    (Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
    College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China)

  • Bo Zheng

    (Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
    College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China)

Abstract

To control the spread of mosquito-borne diseases, one goal of the World Mosquito Program’s Wolbachia release method is to replace wild vector mosquitoes with Wolbachia -infected ones, whose capability of transmitting diseases has been greatly reduced owing to the Wolbachia infection. In this paper, we propose a discrete switching model which characterizes a release strategy including an impulsive and periodic release, where Wolbachia -infected males are released with the release ratio α 1 during the first N generations, and the release ratio is α 2 from the ( N + 1 ) -th generation to the T -th generation. Sufficient conditions on the release ratios α 1 and α 2 are obtained to guarantee the existence and uniqueness of nontrivial periodic solutions to the discrete switching model. We aim to provide new methods to count the exact numbers of periodic solutions to discrete switching models.

Suggested Citation

  • Lijie Chang & Yantao Shi & Bo Zheng, 2021. "Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model," Mathematics, MDPI, vol. 9(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2377-:d:642712
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    References listed on IDEAS

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    1. Zheng, Bo & Yu, Jianshe & Xi, Zhiyong & Tang, Moxun, 2018. "The annual abundance of dengue and Zika vector Aedes albopictus and its stubbornness to suppression," Ecological Modelling, Elsevier, vol. 387(C), pages 38-48.
    2. 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 & A. A., 2011. "The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations," Nature, Nature, vol. 476(7361), pages 450-453, August.
    3. 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 & , 2011. "Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission," Nature, Nature, vol. 476(7361), pages 454-457, August.
    4. Xiaoying Zheng & Dongjing Zhang & Yongjun Li & Cui Yang & Yu Wu & Xiao Liang & Yongkang Liang & Xiaoling Pan & Linchao Hu & Qiang Sun & Xiaohua Wang & Yingyang Wei & Jian Zhu & Wei Qian & Ziqiang Yan , 2019. "Incompatible and sterile insect techniques combined eliminate mosquitoes," Nature, Nature, vol. 572(7767), pages 56-61, August.
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