Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process
This paper examines the propagation dynamics of a T-lymphoblastic leukemia virus type Ⅰ (HTLV-1) infection model in a stochastic environment combined with an Ornstein-Uhlenbeck process. In conjunction with the theory of Lyapunov functions, we initially demonstrate the existence of a unique global so...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241728 |
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| author | Yan Ren Yan Cheng Yuzhen Chai Ping Guo |
| author_facet | Yan Ren Yan Cheng Yuzhen Chai Ping Guo |
| author_sort | Yan Ren |
| collection | DOAJ |
| description | This paper examines the propagation dynamics of a T-lymphoblastic leukemia virus type Ⅰ (HTLV-1) infection model in a stochastic environment combined with an Ornstein-Uhlenbeck process. In conjunction with the theory of Lyapunov functions, we initially demonstrate the existence of a unique global solution to the model when initial values are positive. Subsequently, we establish a sufficient condition for the existence of a stochastic model stationary distribution. Based on this condition, the local probability density function expression of the model near the quasi-equilibrium point is solved by combining it with the Fokker-Planck equation. Subsequently, we delineate the pivotal conditions that precipitate the extinction of the disease. Finally, we select suitable data for numerical simulation intending to corroborate the theorem previously established. |
| format | Article |
| id | doaj-art-ce05e23b13f64376bc05c4c71761374d |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-ce05e23b13f64376bc05c4c71761374d2025-01-23T07:53:26ZengAIMS PressAIMS Mathematics2473-69882024-12-01912364443646910.3934/math.20241728Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck processYan Ren0Yan Cheng1Yuzhen Chai2Ping Guo3College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaCollege of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaCollege of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaCollege of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaThis paper examines the propagation dynamics of a T-lymphoblastic leukemia virus type Ⅰ (HTLV-1) infection model in a stochastic environment combined with an Ornstein-Uhlenbeck process. In conjunction with the theory of Lyapunov functions, we initially demonstrate the existence of a unique global solution to the model when initial values are positive. Subsequently, we establish a sufficient condition for the existence of a stochastic model stationary distribution. Based on this condition, the local probability density function expression of the model near the quasi-equilibrium point is solved by combining it with the Fokker-Planck equation. Subsequently, we delineate the pivotal conditions that precipitate the extinction of the disease. Finally, we select suitable data for numerical simulation intending to corroborate the theorem previously established.https://www.aimspress.com/article/doi/10.3934/math.20241728stochastic htlv-1 infection modellyapunov functionergodic stationary distributionprobability density functionextinction |
| spellingShingle | Yan Ren Yan Cheng Yuzhen Chai Ping Guo Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process AIMS Mathematics stochastic htlv-1 infection model lyapunov function ergodic stationary distribution probability density function extinction |
| title | Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process |
| title_full | Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process |
| title_fullStr | Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process |
| title_full_unstemmed | Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process |
| title_short | Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process |
| title_sort | dynamics and density function of a htlv 1 model with latent infection and ornstein uhlenbeck process |
| topic | stochastic htlv-1 infection model lyapunov function ergodic stationary distribution probability density function extinction |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241728 |
| work_keys_str_mv | AT yanren dynamicsanddensityfunctionofahtlv1modelwithlatentinfectionandornsteinuhlenbeckprocess AT yancheng dynamicsanddensityfunctionofahtlv1modelwithlatentinfectionandornsteinuhlenbeckprocess AT yuzhenchai dynamicsanddensityfunctionofahtlv1modelwithlatentinfectionandornsteinuhlenbeckprocess AT pingguo dynamicsanddensityfunctionofahtlv1modelwithlatentinfectionandornsteinuhlenbeckprocess |