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Wolbachia Invasion Dynamics by Integrodifference Equations

Author

Listed:
  • Yijie Li

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Zhiming Guo

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

Abstract

Releasing mosquitoes infected with the endosymbiotic bacterium Wolbachia to invade and replace the wild populations can effectively interrupt dengue transmission. Recently, a reasonable discrete competitive non-spatial model was developed and the conditions for the successful invasion of Wolbachia were given. However, Wolbachia propagation is a matter of spatial dynamics. In this paper, we introduce a dispersal kernel and establish integrodifference equations, a class of discrete-time spatial diffusion systems that have recently gained much attention as an important tool for spatial ecology. We analyzed the spatial model by average dispersal success approximation to find the criteria for the successful spread of Wolbachia , and then compared it with the non-spatial model to discuss the effect of spatial parameters.

Suggested Citation

  • Yijie Li & Zhiming Guo, 2022. "Wolbachia Invasion Dynamics by Integrodifference Equations," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4253-:d:971862
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    References listed on IDEAS

    as
    1. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    2. 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.
    3. 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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