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In this paper, the dynamical behavior of a stochastic SQEIAR epidemic model is investigated. First of all, we establish sufficient conditions for extinction of the diseases. Then the sufficient conditions for the existence of an ergodic stationary distribution of the positive solutions to the model are obtained by constructing a suitable stochastic Lyapunov function. The existence of stationary distribution implies stochastic weak stability. Furthermore, the optimal control problem is considered to provide a theoretical basis for the prevention and control of the disease. Finally, the theoretical results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered. We first show the existence of the global positive solution, then discuss the effects of noises on the extinction of the species and the stochastic persistence of the species. In the meanwhile, numerical simulations are carried to support results. Finally, we show the existence of the stationary distribution for a special case. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases. Nonlinear incidence and vaccination strategies are also considered in the proposed model. By using the method of stochastic analysis, we point out the key parameters that determine the persistence and extinction of the diseases. Specifically, if Rs 0 is greater than 0, the stochastic system has a unique ergodic stationary distribution; while if R* 0 is less than 0, the diseases will be extinct at an exponential rate. [ABSTRACT FROM AUTHOR]

We investigate a stochastic heroin epidemic model with bilinear incidence and varying population size. Sufficient criteria for the extinction of the drug abusers and the existence of ergodic stationary distribution for the model are established by constructing suitable stochastic Lyapunov functions. By analyzing the sensitivity of the threshold of spread, we obtain that prevention is better than cure. Numerical simulations are carried out to confirm the analytical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the dynamics of a susceptible-infective-latent-infective (SILI) epidemic model that is subject to the combined effects of environmental noise and intervention strategy. We extend the classical SILI epidemic model from a deterministic framework to a stochastic one. For the deterministic case, the global stability analysis of the solution is carried out in terms of the basic reproduction number. For the stochastic case, sufficient conditions for the extinction of diseases are obtained. Then, the existence of stationary distribution and asymptotic behavior of the solution are further studied to illustrate the cycling phenomena of recurrent diseases. Numerical simulations are conducted to verify these analytical results. It is shown that both stochastic noise and intervention strategy contribute to the control of diseases. [ABSTRACT FROM AUTHOR]

In this paper, we explore the long time behavior of a multigroup Susceptible-Infected-Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results. [ABSTRACT FROM AUTHOR]