Threshold behavior in a stochastic HTLV‐I infection model with CTL immune response and regime switching

Abstract

We investigate the stochastic HTLV-I infection model with CTL immune response, which is disturbed by both white and telegraph noises. First, we obtain that the model solution is positive and global. Furthermore, we obtain the existence of ergodic stationary distribution of the solution by stochastic Lyapunov functions with regime switching, and we also establish sufficient conditions for the extinction of system with regime switching. Meanwhile, the threshold R * 0 between ergodic property and extinction of the stochastic system is acquired.Finally, our theoretical results are verified by numerical simulation. KEYWORDS ergodic property, Lyapunov functions, Markov switching, stochastic HTLV-I infection model, threshold ⎧ ⎪ ⎨ ⎪ ⎩̇x6866

On the Dynamics Behaviors of a Stochastic Echinococcosis Infection Model with Environmental Noise

“…Proof. Using the same method as [17], when the local solution of the system (2) is global with the initial value…”

“…Actually, in the real world, environmental noise is an inevitable important factor, so the epidemic model will be affected by environmental noise [13][14][15][16][17][18][19][20]. In this paper, we will consider a type of environmental noise (namely white noise) with the system (1).…”

Dynamics of stochastic HTLV‐I infection model with nonlinear CTL immune response

“…23 Therefore, the existence of stationary distribution has attracted lots of researchers' attention in the recent years. 1,11,20,[24][25][26][27][28] As we can see, to prove the existence of stationary distribution, it is usually the discussion about the nonpositiveness of the Khasminskii-Lyapunov function that is outside of the sufficiently large closed set with the action diffusion operator, which is like to literatures. 11,20,24 Some recent studies [26][27][28] have shown that we can discuss the existence of stationary distribution based on a bounded set when the solution of stochastic system is bounded.…”

Threshold Dynamics of a Non-Linear Stochastic Viral Model with Time Delay and CTL Responsiveness

“…CTLs (Cytotoxic T Lymphocytes) play a significant role in antiviral mechanisms. On the one hand, CTLs imply the main immune factor inhibiting cell that limits the development of virus replication in vivo and depends on viral load [ 11 , 12 , 13 ]; on the other hand, it has recently been demonstrated that infected cells are killed not by the virus but by specific CTLs in some infectious diseases such as hepatitis B [ 3 , 14 ]. Therefore, the dynamics of the epidemic viral model with CTL responsiveness have drawn much attention from researchers in related areas [ 11 , 12 , 13 , 14 , 15 , 16 ].…”