Periodic Orbits of a Mosquito Suppression Model Based on Sterile Mosquitoes

Zhongcai Zhu, Yantao Shi, Rong Yan and Linchao Hu
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Zhongcai Zhu: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Yantao Shi: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Rong Yan: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Linchao Hu: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China

Mathematics, 2022, vol. 10, issue 3, 1-21

Abstract: In this work, we investigate the existence and stability of periodic orbits of a mosquito population suppression model based on sterile mosquitoes. The model switches between two sub-equations as the actual number of sterile mosquitoes in the wild is assumed to take two constant values alternately. Employing the Poincaré map method, we show that the model has at most two T -periodic solutions when the release amount is not sufficient to eradicate the wild mosquitoes, and then obtain some sufficient conditions for the model to admit a unique or exactly two T -periodic solutions. In particular, we observe that the model displays bistability when it admits exactly two T -periodic solutions: the origin and the larger periodic solution are asymptotically stable, and the smaller periodic solution is unstable. Finally, we give two numerical examples to support our lemmas and theorems.

Keywords: sterile mosquitoes; mosquito population suppression; asymptotic stability; periodic solutions; impulsive and periodic release (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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