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<p>A promising avenue to control mosquito-borne diseases such as dengue, malaria, and Zika involves releasing male mosquitoes carrying the bacterium <i>Wolbachia</i> in wild areas to drive female sterility by a mechanism called cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment of how the combined impact of dispersal, incomplete CI and mating competitiveness on mosquito population suppression by a delay differential equation model. Our theoretical analyses indicate that the immigration of eggs plays a significant role in the suppression dynamics. For the case without egg immigration, we identify a threshold dispersal rate <i>v</i>* of adult mosquitoes, threshold CI density <i>ξ</i>*, and threshold release ratio <i>r</i>*. A successful mosquito suppression would be established only when <i>v</i> &lt; <i>v</i>*, <i>ξ</i> &gt; <i>ξ</i>*, and <i>r</i>(<i>t</i>) ≥ <i>r</i>* uniformly. The immigration of eggs causes the threshold dynamics to be invalid, and warns an absolute failure of population suppression. The monotonicity of the adult steady-state in the dispersal rate and CI intensity indicates that choosing a suitable <i>Wolbachia</i> strain with strong CI intensity, or bringing down the dispersal rate of mosquitoes by blocking the suppression zones is a feasible strategy to obtain a better suppression level.</p>

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Global asymptotic stability in a delay stage structured model for mosquito population suppression

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Mu-gen Huang,
  • Jian-she Yu

摘要

A promising avenue to control mosquito-borne diseases such as dengue, malaria, and Zika involves releasing male mosquitoes carrying the bacterium Wolbachia in wild areas to drive female sterility by a mechanism called cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment of how the combined impact of dispersal, incomplete CI and mating competitiveness on mosquito population suppression by a delay differential equation model. Our theoretical analyses indicate that the immigration of eggs plays a significant role in the suppression dynamics. For the case without egg immigration, we identify a threshold dispersal rate v* of adult mosquitoes, threshold CI density ξ*, and threshold release ratio r*. A successful mosquito suppression would be established only when v < v*, ξ > ξ*, and r(t) ≥ r* uniformly. The immigration of eggs causes the threshold dynamics to be invalid, and warns an absolute failure of population suppression. The monotonicity of the adult steady-state in the dispersal rate and CI intensity indicates that choosing a suitable Wolbachia strain with strong CI intensity, or bringing down the dispersal rate of mosquitoes by blocking the suppression zones is a feasible strategy to obtain a better suppression level.