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

1 School of Statistics and Mathematics, Guangdong University of Finance and Economics,Guangzhou 510320, China
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
3 Center for Applied Mathematics,4College of Mathematics and Information Sciences,Guangzhou University, Guangzhou 510006, China

Special Issues: Recent Advances in Mathematical Population Dynamics

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 ξ, and the mating competitiveness µ of released males relative to wild males, impact the suppression efficacy by a delay differential equation model. Our analysis identifies a threshold CI intensity ξ0 ∈ (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 ξ ≤ ξ0 , and succeeds when ξ > ξ0 and r(t) ≥ r . Our analyses indicate that ξ plays a more important role than µ in the population suppression. For instance, a slight decrease of ξ from 1 to 0.92 is more devastating than halving µ 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 µ but is sensitive to ξ. 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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Keywords mosquito-born diseases; Wolbachia; cytoplasmic incompatibility; mosquito population suppression; delay differential equation

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


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