Existence and stability of a unique and exact two periodic orbits for an interactive wild and sterile mosquito model

• Published in: Journal of Differential Equations Vol. 269; no. 12; pp. 10395 - 10415
• Main Author: Yu, Jianshe
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 05.12.2020
• Subjects: Asymptotic stability; At most two periodic solutions; Exact two periodic solutions; Mosquito population suppression; Sterile mosquitoes; Uniqueness; Asymptotic stability; 34C25; 92D30; 34D23; 92D25; Mosquito population suppression; At most two periodic solutions; Sterile mosquitoes; Exact two periodic solutions; Uniqueness; 92D40; 34D05
• ISSN: 0022-0396; 1090-2732
• DOI: 10.1016/j.jde.2020.07.019

In this paper, we study the existence and stability of a unique and exact two periodic orbits of an ordinary differential equation model for the interaction of wild and the released sterile mosquitoes, which consists of two sub-equations constantly switching each other. We first show that the model has at most two periodic solutions for all of the parameters and then surprisingly find that the model has a unique periodic solution if and only if the origin is unstable, and has exact two periodic solutions if and only if the origin is asymptotically stable provided the release amount does not exceed the release amount threshold value, respectively. We also give sufficient conditions for the existence of exact two periodic solutions and analyze the stability of each periodic solution.