Search

In this paper, we study the dynamical behavior of a stochastic two-compartment model of B -cell chronic lymphocytic leukemia, which is perturbed by white noise. Firstly, by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then, conditions for extinction of the disease are derived. Furthermore, numerical simulations are presented for supporting the theoretical results. Our results show that large noise intensity may contribute to extinction of the disease. [ABSTRACT FROM AUTHOR]

In this paper, we consider two chemostat models with random perturbation, in which single species depends on two perfectly substitutable resources for growth. For the autonomous system, we first prove that the solution of the system is positive and global. Then we establish sufficient conditions for the existence of an ergodic stationary distribution by constructing appropriate Lyapunov functions. For the non-autonomous system, by using Has'minskii theory on periodic Markov processes, we derive it admits a nontrivial positive periodic solution. Finally, numerical simulations are carried out to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic chemostat model with single-species growth on two perfectly substitutable nutrients under telegraph noise is investigated. Firstly, we prove the solution of the system is positive and global. Then we establish sufficient conditions for the existence of ergodic stationary distribution of the model by constructing suitable Lyapunov functions with regime switching. Finally, numerical simulations are carried out to demonstrate our theoretical results. • A stochastic chemostat model with two nutrients under telegraph noise is considered. • We establish sufficient conditions for the existence of stationary distribution. • The existence of stationary distribution implies stochastic weak stability. • Numerical simulations are carried out to illustrate the results. [ABSTRACT FROM AUTHOR]

This article focuses on a stochastic viral model with distributed delay and CTL responsiveness. It is shown that the viral disease will be extinct if the stochastic reproductive ratio is less than one. However, when the stochastic reproductive ratio is more than one, the viral infection system consists of an ergodic stationary distribution. Furthermore, we obtain the existence and uniqueness of the global positive solution by constructing a suitable Lyapunov function. Finally, we illustrate our results by numerical simulation. [ABSTRACT FROM AUTHOR]