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 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.