@article{Ren2024, 
author = {Yan Ren and Yan Cheng and Yuzhen Chai and Ping Guo},
title = {Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36444-36469},
keywords = {stochastic HTLV-1 infection model, Lyapunov function, ergodic stationary distribution, probability density function, extinction},
url = {https://www.sciopen.com/article/10.3934/math.20241728},
doi = {10.3934/math.20241728},
abstract = {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.}
}