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1.
In this paper, we investigate the threshold dynamics of a stochastic delayed SIS epidemic model with vaccination and double diseases which make the research more difficult. We establish sufficient conditions for extinction and persistence in the mean of the two diseases. We also obtain the threshold between persistence in the mean and extinction of the stochastic system. It is shown that: (i) time delay and environmental white noise have important effects on the persistence and extinction of the two diseases; (ii) the two diseases can coexist under certain conditions. Finally, some numerical simulations are provided to demonstrate the analytical results.  相似文献   

2.
In this paper, we investigate the dynamical behavior of a stochastic dengue epidemic model. First of all, by constructing a suitable stochastic Lyapunov function, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the diseases. The existence of stationary distribution implies stochastic weak stability.  相似文献   

3.
In this paper, a stochastic epidemic model for cholera is proposed and investigated. Firstly, we establish sufficient conditions for extinction of the disease. Then we establish sufficient criteria for the existence of a unique ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The existence of an ergodic stationary distribution implies that all the individuals can be coexistent in the long run. Finally, some examples together with numerical simulations are introduced to illustrate our theoretical results.  相似文献   

4.
In this paper, we consider a stochastic multigroup SIQR epidemic model with standard incidence rates. By using the stochastic Lyapunov function method, we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the diseases. A stationary distribution means that all the individuals can be coexistent and persistent in the long term. Finally, some examples and numerical simulations are introduced to illustrate our theoretical results.  相似文献   

5.
In this paper, we study a stochastic SIR epidemic model with distributed delay and degenerate diffusion. Firstly, we transform the stochastic model into an equivalent system which contains three equations. Since the diffusion matrix is degenerate, the uniform ellipticity condition is not satisfied. The Markov semigroup theory is used to obtain the existence and uniqueness of a stable stationary distribution. We verify the densities of the distributions of the solutions can converge in L1 to an invariant density. Then we establish sufficient conditions for extinction of the disease. Some examples and numerical simulations are introduced to illustrate our analytical results.  相似文献   

6.
In this paper, we propose and study a stochastic predator–prey model with herd behavior. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases, that is, the first case is the prey population survival and the predator population extinction; the second case is all the prey and predator populations extinction. Finally, some examples together with numerical simulations are introduced to illustrate the theoretical results.  相似文献   

7.
In this paper a delayed stochastic SLVIQR epidemic model, which can be applied for modeling the new coronavirus COVID-19 after a calibration, is derived. Model is constructed by assuming that transmission rate satisfies the mean-reverting Ornstain-Uhlenbeck process and, besides a standard Brownian motion, another two driving processes are considered: a stationary Poisson point process and a continuous finite-state Markov chain. For the constructed model, the existence and uniqueness of positive global solution is proven. Also, sufficient conditions under which the disease would lead to extinction or be persistent in the mean are established and it is shown that constructed model has a richer dynamic analysis compared to existing models. In addition, numerical simulations are given to illustrate the theoretical results.  相似文献   

8.
This paper is concerned with Lotka–Volterra models formulated using stochastic differential equations with regime switching represented by a continuous-time Markov chain. Different from the existing literature, the Markov chain is hidden and can only be observed in a Gaussian white noise in our work. For such partially observed problems, we use a Wonham filter to estimate the Markov chain from the observable evolution of the given process, and convert the original system to a completely observable one. We then establish the regularity, positivity, stochastic boundedness, and sample path continuity of the solution. Moreover, stochastic permanence and extinction using feedback controls are investigated. Numerical experiments are conducted to validate the theoretical findings and demonstrate how feedback controls perform in practice.  相似文献   

9.
This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.  相似文献   

10.
This paper is denoted to investigating stability in mean of partial variables for stochastic reaction–diffusion equations with Markovian switching (SRDEMS). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations with Markovian switching (SODEMS) and using Itô formula, sufficient criteria on uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, exponential stability in mean of partial variables for SRDEMS are first derived. An example is presented to illustrate the effectiveness and efficiency of the obtained results.  相似文献   

11.
在现有文献的基础上，对一类马尔可夫调制的随机微分方程进行了研究，得到了其平凡解2阶均值指数稳定性和几乎必然指数稳定性的充分条件。对现有成果进行了改进。  相似文献   

12.
In this paper, the pth moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching is investigated. Based on the Lyapunov function, Dynkin formula and Razumikhin technique with stochastic version as well as stochastic analysis theory, many new sufficient conditions are derived to ensure the pth moment exponential stability of the trivial solution. The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses. Moreover, our results generalize and improve some results obtained in the literature. Finally, a numerical example and its simulations are given to illustrate the theoretical results.  相似文献   

13.
In this study, we develop a vector-host transmission model with general incidence rates for the dynamics of pine wilt disease in deterministic and stochastic environments. The existence and local asymptotic stability of equilibria are investigated in the deterministic case. We show the required conditions for the ergodic stationary distribution and extinction of the model in the stochastic case by constructing appropriate Lyapunov functions. Furthermore, by solving the corresponding Fokker-Planck equation, we obtain exact expressions of probability density function around the quasi-equilibrium of the stochastic model. Finally, we employ comprehensive numerical simulations to support our results and compare deterministic and stochastic situations.  相似文献   

14.
Parameters of mathematical models are often imprecise due to various uncertainties. How parameter imprecision and sudden environmental changes influence the optimal control of dynamical systems remains unclear. In this paper, we formulate an Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model that includes imprecise parameters, Lévy jumps, and vaccination control. We use the model to investigate the near-optimal control problem in the setting of vaccination. We obtain priori estimates of the susceptible, infected and recovered populations. We establish sufficient and necessary conditions for the near-optimality of the model using Pontryagin stochastic maximum principle. We also develop an algorithm for the near-optimal control problem and perform numerical simulations to illustrate the effect of vaccination and Lévy noise.  相似文献   

15.
In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples.  相似文献   

16.
We consider the leader–follower consensus problem for a multi-agent system where information is exchanged only on a non-uniform discrete stochastic time domain. For a second-order multi-agent system subject to intermittent information exchange, we model the tracking error dynamics as a μ?varying linear system on a discrete stochastic time scale, where μ is the graininess operator. Based on a Lyapunov operator and a positive perturbation operator on the space of symmetric matrices, we derive necessary and sufficient conditions to design a decentralized consensus protocol. This protocol allows us to cast the mean-square exponential consensus problem within the framework of dynamic equations on stochastic time scales. We establish some theoretical results which allow for the computation of the control gain matrix which guarantees the mean-square exponential stability with a given decay rate for the error dynamics. To show the effectiveness of the theoretical results, some simulation and experimental results on multi-robot systems have been performed.  相似文献   

17.
胡志军  李略 《大众科技》2013,(6):226-227
文章中首先得到一个稠密性结果,然后利用标量化方法,建立了集值映射下的参数广义强向量平衡问题解映射的下半连续性。  相似文献   

18.
This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses.  相似文献   

19.
In this paper, a discrete-time interval general BAM bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we establish new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the discrete-time interval general BAM bidirectional neural networks. The results obtained generalize and improve known results in [23]. An example is provided to show the correctness of our analysis.  相似文献   

20.
This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.  相似文献   

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