Mathematical Biosciences and Engineering

2019, Issue 5: 4741-4757. doi: 10.3934/mbe.2019238
Research article Special Issues

The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachia-driven mosquito population suppressio

• Received: 28 November 2018 Accepted: 14 May 2019 Published: 27 May 2019
• To control mosquito-borne diseases such as dengue, malaria, and Zika, Wolbachia-infected male mosquitoes have been released in open areas to suppress wild mosquito population driven by cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment on how the CI intensity $\xi$, and the mating competitiveness $\mu$ of released males relative to wild males, impact the suppression efficacy by a delay differential equation model. Our analysis identifies a threshold CI intensity $\xi_0\in (0, 1)$ as an increasing function of the natural reproduction rate of the wild mosquitoes, and a threshold value $r^*$ for the ratio $r(t)$ between the numbers of released males and wild males. The population suppression fails when $\xi\le \xi_0$, and succeeds when $\xi>\xi_0$ and $r(t)\ge r^*$. Our analyses indicate that $\xi$ plays a more important role than $\mu$ in the population suppression. For instance, a slight decrease of $\xi$ from 1 to 0.92 is more devastating than halving $\mu$ from 1 to 0.5. In our estimation of the optimal starting date for infected male release to target a more than $95\%$ wild population reduction during the peak season of dengue in Guangzhou, we find that the optimal date is almost independent of $\mu$ but is sensitive to $\xi$. If CI is complete, then starting about two months ahead can be an optimal option for less financial and labor costs. A slight reduction in the CI intensity requires a considerably earlier starting date.

Citation: Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachia-driven mosquito population suppressio[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4741-4757. doi: 10.3934/mbe.2019238

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• To control mosquito-borne diseases such as dengue, malaria, and Zika, Wolbachia-infected male mosquitoes have been released in open areas to suppress wild mosquito population driven by cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment on how the CI intensity $\xi$, and the mating competitiveness $\mu$ of released males relative to wild males, impact the suppression efficacy by a delay differential equation model. Our analysis identifies a threshold CI intensity $\xi_0\in (0, 1)$ as an increasing function of the natural reproduction rate of the wild mosquitoes, and a threshold value $r^*$ for the ratio $r(t)$ between the numbers of released males and wild males. The population suppression fails when $\xi\le \xi_0$, and succeeds when $\xi>\xi_0$ and $r(t)\ge r^*$. Our analyses indicate that $\xi$ plays a more important role than $\mu$ in the population suppression. For instance, a slight decrease of $\xi$ from 1 to 0.92 is more devastating than halving $\mu$ from 1 to 0.5. In our estimation of the optimal starting date for infected male release to target a more than $95\%$ wild population reduction during the peak season of dengue in Guangzhou, we find that the optimal date is almost independent of $\mu$ but is sensitive to $\xi$. If CI is complete, then starting about two months ahead can be an optimal option for less financial and labor costs. A slight reduction in the CI intensity requires a considerably earlier starting date.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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