Dynamic Analysis of a Stochastic Rumor Propagation Model with Regime Switching

We study the rumor propagation model with regime switching considering both colored and white noises. Firstly, by constructing suitable Lyapunov functions, the sufficient conditions for ergodic stationary distribution and extinction are obtained. Then we obtain the threshold Rs which guarantees the extinction and the existence of the stationary distribution of the rumor. Finally, numerical simulations are performed to verify our model. The results indicated that there is a unique ergodic stationary distribution when Rs>1. The rumor becomes extinct exponentially with probability one when Rs<1.

Global Dynamics of a Stochastic Viral Infection Model with Latently Infected Cells

In this paper, we study the global dynamics of a stochastic viral infection model with humoral immunity and Holling type II response functions. The existence and uniqueness of non-negative global solutions are derived. Stationary ergodic distribution of positive solutions is investigated. The solution fluctuates around the equilibrium of the deterministic case, resulting in the disease persisting stochastically. The extinction conditions are also determined. To verify the accuracy of the results, numerical simulations were carried out using the Euler–Maruyama scheme. White noise’s intensity plays a key role in treating viral infectious diseases. The small intensity of white noises can maintain the existence of a stationary distribution, while the large intensity of white noises is beneficial to the extinction of the virus.

Removal of Gaussian White Noises from the image by probability map prediction based Deep learning approach

Deep learning methods have gained an increasing research interest, especially in the field of image denoising. Although there are significant differences between the different types of deep learning techniques used for natural image denoising, it includes significant process and procedure differences between them. To be specific, discriminative learning based on deep learning convolutional neural network (CNN) may effectively solve the problem of Gaussian noise. Deep learning based optimization models are useful in predicting the true noise level. However, no relevant research has attempted to summarize the different deep learning approaches for performing image denoising in one location. It has been suggested to build the proposed framework in parallel with the previously trained CNN to enhance the training speed and accuracy in denoising the Gaussian White Noise (GWN). In the proposed architecture, ground truth maps are created by combining the additional patches of input with original pictures to create ground truth maps. Furthermore, by changing kernel weights for forecasting probability maps, the loss function may be reduced to its smallest value. Besides, it is efficient in terms of processing time with less sparsity while enlarging the objects present in the images. As well as in conventional methods, various performance measures such as PSNR, MSE, and SSIM are computed and compared with one another.

Mean-square exponential input-to-state stability of stochastic inertial neural networks

By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments. Constructing two Lyapunov–Krasovskii functionals, we establish the mean-square exponential input-to-state stability on the addressed model, which generalizes and refines the recent results. In addition, an example with numerical simulation is carried out to support the theoretical findings.

Dynamics of a stochastic delayed avian influenza model with mutation and temporary immunity

In this paper, the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity. First, we prove the existence and uniqueness of the global positive solution for the stochastic model. Second, we give two different thresholds [Formula: see text] and [Formula: see text], and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system, respectively. Compared with the corresponding deterministic model, the thresholds affected by the white noises are smaller than the ones of the deterministic system. Finally, numerical simulations are carried out to support our theoretical results. It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations, while prompt the spread of mutant avian influenza in human population.