Journal
ADVANCES IN NONLINEAR ANALYSIS
Volume 11, Issue 1, Pages 212-224Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/anona-2020-0194
Keywords
Discrete model; Wolbachia infection frequency; Mosquito population; Existence and uniqueness; Periodic orbits
Categories
Funding
- National Natural Science Foundation of China [11971127, 12071095, 11631005]
- Program for Changjiang Scholars and Innovative Research Team in University [IRT_16R16]
Ask authors/readers for more resources
This paper studies a discrete model on Wolbachia infection frequency and proposes a periodic and impulsive release strategy. For specific parameter values, the existence of periodic solutions and the stability of a unique solution for the model are proven.
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 alpha, and the release is terminated from (N + 1)-th generation to T-th generation. We find a release ratio threshold denoted by alpha* (N , T), and prove the existence of a T-periodic solution for the model when alpha is an element of (0, alpha* (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 alpha is an element of (0, alpha* (N, T)). While alpha >= alpha* (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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available