Modeling and analysis of the implementation of the Wolbachia incompatible and sterile insect technique for mosquito population suppression.

B. Zheng, J. S. Yu and J. Li,  Siam Journal on Applied Mathematics,  81:718-740. 2021.

The release of Wolbachia-infected mosquitoes in 2016 and 2017 enabled near-elimination of the sole dengue vector Aedes albopictus on Shazai and Dadaosha islands in Guangzhou. Mathematical analysis may offer guidance in designing effective mass release strategies for the area-wide application of this Wolbachia incompatible and sterile insect technique in the future. The two most crucial concerns in designing release strategies are how often and in what amount should Wolbachia-infected mosquitoes be released in order to guarantee population suppression. Motivated by the experimental data from the Guangzhou mosquito factory and the release strategy implemented on two islands, we formulate and analyze a mosquito population suppression model considering the situation for the release period T less than the sexual lifespan of Wolbachia-infected males. We define release amount thresholds g(1)* and g(2)* with g(1)* < g(2)*. When the release amount c satisfies c >= g(2)*, population suppression is always achievable, as is mathematically manifested by the global asymptotic stability of the origin. However, when c is an element of (0, g(1)*], we find that suppression can be achieved only if the initial wild mosquito population is small enough. This is mathematically proved by the local asymptotic stability of the origin, together with the existence of exactly two T-periodic solutions, one of which is asymptotically stable and the other of which is unstable, with T being the waiting period between two consecutive releases. For c is an element of (g(1)*, g(2)*), we find sufficient conditions on the nonexistence of T-periodic solution, and the existence of at most two T-periodic solutions.

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