Global dynamics of an impulsive vector-borne disease model with time delays
In this paper, we investigate a time-delayed vector-borne disease model with impulsive culling of the vector. The basic reproduction number $ \mathcal{R}_0 $ of our model is first introduced by the theory recently established in <sup>[<xref ref-type="bibr" rid="b1">1&...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-11-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023926?viewType=HTML |
| _version_ | 1797397640971812864 |
|---|---|
| author | Rong Ming Xiao Yu |
| author_facet | Rong Ming Xiao Yu |
| author_sort | Rong Ming |
| collection | DOAJ |
| description | In this paper, we investigate a time-delayed vector-borne disease model with impulsive culling of the vector. The basic reproduction number $ \mathcal{R}_0 $ of our model is first introduced by the theory recently established in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Then the threshold dynamics in terms of $ \mathcal{R}_0 $ are further developed. In particular, we show that if $ \mathcal{R}_0 < 1 $, then the disease will go extinct; if $ \mathcal{R}_0 > 1 $, then the disease will persist. The main mathematical approach is based on the uniform persistent theory for discrete-time semiflows on some appropriate Banach space. Finally, we carry out simulations to illustrate the analytic results and test the parametric sensitivity on $ \mathcal{R}_0 $. |
| first_indexed | 2024-03-09T01:13:04Z |
| format | Article |
| id | doaj.art-d04011fc95594404a471812f9cdef015 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-03-09T01:13:04Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-d04011fc95594404a471812f9cdef0152023-12-11T01:28:51ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-11-012012209392095810.3934/mbe.2023926Global dynamics of an impulsive vector-borne disease model with time delaysRong Ming0Xiao Yu1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaSchool of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaIn this paper, we investigate a time-delayed vector-borne disease model with impulsive culling of the vector. The basic reproduction number $ \mathcal{R}_0 $ of our model is first introduced by the theory recently established in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Then the threshold dynamics in terms of $ \mathcal{R}_0 $ are further developed. In particular, we show that if $ \mathcal{R}_0 < 1 $, then the disease will go extinct; if $ \mathcal{R}_0 > 1 $, then the disease will persist. The main mathematical approach is based on the uniform persistent theory for discrete-time semiflows on some appropriate Banach space. Finally, we carry out simulations to illustrate the analytic results and test the parametric sensitivity on $ \mathcal{R}_0 $.https://www.aimspress.com/article/doi/10.3934/mbe.2023926?viewType=HTMLvector-bornebasic reproduction numbertime delaythreshold dynamicsperiodic culling |
| spellingShingle | Rong Ming Xiao Yu Global dynamics of an impulsive vector-borne disease model with time delays Mathematical Biosciences and Engineering vector-borne basic reproduction number time delay threshold dynamics periodic culling |
| title | Global dynamics of an impulsive vector-borne disease model with time delays |
| title_full | Global dynamics of an impulsive vector-borne disease model with time delays |
| title_fullStr | Global dynamics of an impulsive vector-borne disease model with time delays |
| title_full_unstemmed | Global dynamics of an impulsive vector-borne disease model with time delays |
| title_short | Global dynamics of an impulsive vector-borne disease model with time delays |
| title_sort | global dynamics of an impulsive vector borne disease model with time delays |
| topic | vector-borne basic reproduction number time delay threshold dynamics periodic culling |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023926?viewType=HTML |
| work_keys_str_mv | AT rongming globaldynamicsofanimpulsivevectorbornediseasemodelwithtimedelays AT xiaoyu globaldynamicsofanimpulsivevectorbornediseasemodelwithtimedelays |