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Modeling and dynamics of Wolbachia-infected male releases and mating competition on mosquito control

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Abstract

Despite centuries of continuous efforts, mosquito-borne diseases (MBDs) remain enormous health threat of human life worldwide. Lately, the USA government has approved an innovative technology of releasing Wolbachia-infected male mosquitoes to suppress the wild mosquito population. In this paper we first introduce a stage-structured model for natural mosquitos, then we establish a new model considering the releasing of Wolbachia-infected male mosquitoes and the mating competition between the natural male mosquitoes and infected males on the suppression of natural mosquitoes. Dynamical analysis of the two models, including the existence and local stability of the equilibria and bifurcation analysis, reveals the existence of a forward bifurcation or a backward bifurcation with multiple attractors. Moreover, globally dynamical properties are further explored by using Lyapunov function and theory of monotone operators, respectively. Our findings suggest that infected male augmentation itself cannot always guarantee the success of population eradication, but leads to three possible levels of population suppression, so we define the corresponding suppression rate and estimate the minimum release ratio for population eradication. Furthermore, we study how the release ratio of infected males and natural ones, mating competition, the rate of cytoplasmic incompatibility and the basic offspring number affect the suppression rate of natural mosquitoes. Our results show that the successful eradication relies on assessing the reproductive capacity of natural mosquitoes, a selection of suitable Wolbachia strains and an appropriate release amount of infected males. This study will be helpful for public health authorities in designing proper strategies to control vector mosquitoes and prevent the epidemics of MBDs.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC, 61772017), the Doctoral Fund of Southwest University (No. SWU019046) and the NSERC and CIHR of Canada.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Xianghong Zhang

  2. LAMPS and CDM, Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    Xianghong Zhang & Huaiping Zhu

  3. State Key Laboratory of Infectious Disease Prevention and Control, National Institute for Communicable Disease Control and Prevention, Chinese Center for Disease Control and Prevention, Beijing, 102206, People’s Republic of China

    Qiyong Liu

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  1. Xianghong Zhang
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Correspondence to Huaiping Zhu.

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Zhang, X., Liu, Q. & Zhu, H. Modeling and dynamics of Wolbachia-infected male releases and mating competition on mosquito control. J. Math. Biol. 81, 243–276 (2020). https://doi.org/10.1007/s00285-020-01509-7

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  • DOI: https://doi.org/10.1007/s00285-020-01509-7

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