Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, People's Republic of China.
Department of Mathematical Sciences, The University of Alabama in Huntsville, Huntsville, AL, 35899, USA.
Bull Math Biol. 2022 Sep 16;84(11):121. doi: 10.1007/s11538-022-01073-9.
Due to the role of cytoplasmic incompatibility (CI), releasing Wolbachia-infected male mosquitoes into the wild becomes a very promising strategy to suppress the wild mosquito population. When developing a mosquito suppression strategy, our main concerns are how often, and in what amount, should Wolbachia-infected mosquitoes be released under different CI intensity conditions, so that the suppression is most effective and cost efficient. In this paper, we propose a mosquito population suppression model that incorporates suppression and self-recovery under different CI intensity conditions. We adopt the new modeling idea that only sexually active Wolbachia-infected male mosquitoes are considered in the model and assume the releases of Wolbachia-infected male mosquitoes are impulsive and periodic with period T. We particularly study the case where the release period is greater than the sexual lifespan of the Wolbachia-infected male mosquitoes. We define the CI intensity threshold, mosquito release thresholds, and the release period threshold to characterize the model dynamics. The global and local asymptotic stability of the origin and the existence and stability of T-periodic solutions are investigated. Our findings provide useful guidance in designing practical release strategies to control wild mosquitoes.
由于细胞质不亲和性（CI）的作用，将感染沃尔巴克氏体的雄性蚊子释放到野外成为一种非常有前途的抑制野生蚊子种群的策略。在制定蚊子抑制策略时，我们主要关注的是在不同 CI 强度条件下，应该以多高的频率和多大的数量释放感染沃尔巴克氏体的蚊子，才能使抑制效果最有效和成本效益最高。在本文中，我们提出了一个蚊子种群抑制模型，该模型考虑了不同 CI 强度条件下的抑制和自我恢复。我们采用了一个新的建模思路，即仅考虑具有性活力的感染沃尔巴克氏体的雄性蚊子，并假设释放感染沃尔巴克氏体的雄性蚊子是脉冲式的，且具有周期 T。我们特别研究了释放周期大于感染沃尔巴克氏体的雄性蚊子的性寿命的情况。我们定义了 CI 强度阈值、蚊子释放阈值和释放周期阈值来描述模型动态。研究了原点的全局和局部渐近稳定性以及 T-周期解的存在性和稳定性。我们的研究结果为设计控制野生蚊子的实际释放策略提供了有用的指导。
