Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency
In this paper, we study a discrete model on infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected males are released during the first generations with the release ratio , and the release is terminated from ( + 1)-th generation to -th generation. We...
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| Published in | Advances in nonlinear analysis Vol. 11; no. 1; pp. 212 - 224 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.01.2022
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2191-9496 2191-950X 2191-950X |
| DOI | 10.1515/anona-2020-0194 |
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| Abstract | In this paper, we study a discrete model on
infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected males are released during the first
generations with the release ratio
, and the release is terminated from (
+ 1)-th generation to
-th generation. We find a release ratio threshold denoted by
,
), and prove the existence of a
-periodic solution for the model when
(0,
,
)). For the special case when
= 1 and
= 2, we prove that the model has a unique
-periodic solution which is unstable when
(0,
,
)). While
≥
,
), no periodic phenomenon occurs and the
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. |
|---|---|
| AbstractList | In this paper, we study a discrete model on
infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected males are released during the first
generations with the release ratio
, and the release is terminated from (
+ 1)-th generation to
-th generation. We find a release ratio threshold denoted by
,
), and prove the existence of a
-periodic solution for the model when
(0,
,
)). For the special case when
= 1 and
= 2, we prove that the model has a unique
-periodic solution which is unstable when
(0,
,
)). While
≥
,
), no periodic phenomenon occurs and the
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. 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. 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. |
| Author | Yu, Jianshe Zheng, Bo |
| Author_xml | – sequence: 1 givenname: Bo surname: Zheng fullname: Zheng, Bo email: zhengbo611@outlook.com organization: Center for Applied Mathematics, College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China – sequence: 2 givenname: Jianshe surname: Yu fullname: Yu, Jianshe email: jsyu@gzhu.edu.cn organization: Center for Applied Mathematics, College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China |
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| Snippet | In this paper, we study a discrete model on
infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected males are... In this paper, we study a discrete model on Wolbachia infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected... In this paper, we study a discrete model on Wolbachia infection frequency. Assume that a periodic and impulsive release strategy is implemented, where infected... |
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| SubjectTerms | 37N25 92B05 92D30 Discrete model Existence and uniqueness infection frequency Mosquito population Periodic orbits wolbachia infection frequency |
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| Title | Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency |
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