Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency

Advances in Nonlinear Analysis

article

Bo Zheng¹  Jianshe Yu¹ 

[1] Center for Applied Mathematics, College of Mathematics and Information Sciences, Guangzhou University

关键词: Discrete model;    Wolbachia infection frequency;    Mosquito population;    Existence and uniqueness;    Periodic orbits;   

DOI  :  10.1515/anona-2020-0194

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we study a discrete model on Wolbachia infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected males are released during the first N generations with the release ratio α , and the release is terminated from ( N + 1)-th generation to T -th generation. We find a release ratio threshold denoted by α * ( N , T ), and prove the existence of a T -periodic solution for the model when α ∈ (0, α * ( N , T )). For the special case when N = 1 and T = 2, we prove that the model has a unique T -periodic solution which is unstable when α ∈ (0, α * ( N , T )). While α ≥ α * ( N , T ), no periodic phenomenon occurs and the Wolbachia fixation equilibrium is globally asymptotically stable. Numerical simulations are also provided to illustrate our theoretical results. One main contribution of this work is to offer a new method to determine the exact number of periodic orbits to discrete models.

【 授权许可】

CC BY