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

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...

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Autores principales:	Zheng Bo, Yu Jianshe
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	discrete model wolbachia infection frequency mosquito population existence and uniqueness periodic orbits 92b05 92d30 37n25 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/9d52b99335aa48208375667131aba9af
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spelling	oai:doaj.org-article:9d52b99335aa48208375667131aba9af2021-12-05T14:10:40ZExistence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency2191-94962191-950X10.1515/anona-2020-0194https://doaj.org/article/9d52b99335aa48208375667131aba9af2021-07-01T00:00:00Zhttps://doi.org/10.1515/anona-2020-0194https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XIn 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.Zheng BoYu JiansheDe Gruyterarticlediscrete modelwolbachia infection frequencymosquito populationexistence and uniquenessperiodic orbits92b0592d3037n25AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 212-224 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	discrete model wolbachia infection frequency mosquito population existence and uniqueness periodic orbits 92b05 92d30 37n25 Analysis QA299.6-433
spellingShingle	discrete model wolbachia infection frequency mosquito population existence and uniqueness periodic orbits 92b05 92d30 37n25 Analysis QA299.6-433 Zheng Bo Yu Jianshe Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
description	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.
format	article
author	Zheng Bo Yu Jianshe
author_facet	Zheng Bo Yu Jianshe
author_sort	Zheng Bo
title	Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
title_short	Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
title_full	Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
title_fullStr	Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
title_full_unstemmed	Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
title_sort	existence and uniqueness of periodic orbits in a discrete model on wolbachia infection frequency
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/9d52b99335aa48208375667131aba9af
work_keys_str_mv	AT zhengbo existenceanduniquenessofperiodicorbitsinadiscretemodelonwolbachiainfectionfrequency AT yujianshe existenceanduniquenessofperiodicorbitsinadiscretemodelonwolbachiainfectionfrequency
_version_	1718371854682423296

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

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