Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response
Abstract In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02911-7 |
| _version_ | 1819133591091675136 |
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| author | Suxia Wang Juan Zhao Junxing Zhu Xiaoli Ren |
| author_facet | Suxia Wang Juan Zhao Junxing Zhu Xiaoli Ren |
| author_sort | Suxia Wang |
| collection | DOAJ |
| description | Abstract In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results. |
| first_indexed | 2024-12-22T09:49:43Z |
| format | Article |
| id | doaj.art-67fe03e223e74f9d992533e33b232bac |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T09:49:43Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-67fe03e223e74f9d992533e33b232bac2022-12-21T18:30:25ZengSpringerOpenAdvances in Difference Equations1687-18472020-09-012020111410.1186/s13662-020-02911-7Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional responseSuxia Wang0Juan Zhao1Junxing Zhu2Xiaoli Ren3College of Computer Meteorology and Oceanography, National University of Defense TechnologyCollege of Computer Meteorology and Oceanography, National University of Defense TechnologyCollege of Computer Meteorology and Oceanography, National University of Defense TechnologyCollege of Computer Meteorology and Oceanography, National University of Defense TechnologyAbstract In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.http://link.springer.com/article/10.1186/s13662-020-02911-7Stochastic HIV modelItô’s formulaAsymptotic behaviorLyapunov functionBeddington–DeAngelis functional |
| spellingShingle | Suxia Wang Juan Zhao Junxing Zhu Xiaoli Ren Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response Advances in Difference Equations Stochastic HIV model Itô’s formula Asymptotic behavior Lyapunov function Beddington–DeAngelis functional |
| title | Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response |
| title_full | Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response |
| title_fullStr | Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response |
| title_full_unstemmed | Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response |
| title_short | Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response |
| title_sort | asymptotic behavior of a stochastic hiv model with beddington deangelis functional response |
| topic | Stochastic HIV model Itô’s formula Asymptotic behavior Lyapunov function Beddington–DeAngelis functional |
| url | http://link.springer.com/article/10.1186/s13662-020-02911-7 |
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