ANALYSIS OF A SUSCEPTIBLE-EXPOSEDINFECTED EPIDEMIC MODEL WITH RANDOM PERTURBATION AND VARYING POPULATION SIZE

In this paper, we study a type of susceptible-exposed-infected(SEI) epidemic model with varying population size and introduce the random perturbation of the constant contact rate into the SEI epidemic model due to the universal existence of fluctuations. Under some moderate conditions, the density of the exposed and the infected individuals exponentially approaches zero almost surely are derived. Furthermore, the stochastic SEI epidemic model admits a stationary distribution around the endemic equilibrium, and the solution is ergodic. Some numerical simulations are carried out to demonstrate the efficiency of the main results.

Privacy-Preserving Recommendation Based on Kernel Method in Cloud Computing

The application field of the Internet of Things(IoT)involves all aspects,and its application in the fields of industry,agriculture,environment,transportation,logistics,security and other infrastructure has effectively promoted the intelligent development of these aspects.Although the IoT has gradually grown in recent years,there are still many problems that need to be overcome in terms of technology,management,cost,policy,and security.We need to constantly weigh the benefits of trusting IoT products and the risk of leaking private data.To avoid the leakage and loss of various user data,this paper developed a hybrid algorithm of kernel function and random perturbation method based on the algorithm of non-negative matrix factorization,which realizes personalized recommendation and solves the problem of user privacy data protection in the process of personalized recommendation.Compared to non-negative matrix factorization privacy-preserving algorithm,the new algorithm does not need to know the detailed information of the data,only need to know the connection between each data;and the new algorithm can process the data points with negative characteristics.Experiments show that the new algorithm can produce recommendation results with certain accuracy under the premise of preserving users’personal privacy.

Ergodic stationary distribution of two stochastic tuberculosis models with imperfect vaccination and early and late latency

This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises and color noises on TB control in random environments.We first investigate the existence and uniqueness of ergodic stationary distribution(EUESD)for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions,and suficient conditions on the extinction of disease are acquired.Next,sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established.Eventually,some numerical examples validate the theoretical findings.What's more,it has been observed that higher amplitude noises may lead to the eradication of TB,which is conducive to TB control.

High-order numerical method for the derivative nonlinear Schrodinger equation

In this work,a fourth-order numerical scheme in space and two second-order numerical schemes in both time and space are proposed for the derivative nonlinear Schrodinger equation.We verify the mass conservation for the two-level implicit scheme.The influence on the soliton solution by adding a small random perturbation to the initial condition is discussed.The numerical experiments are given to test the accuracy order for different schemes,respectively.We also test the conservative property of mass and Hamiltonian for these schemes from the numerical point of view.

LONG-TERM DYNAMIC ANALYSIS OF ENDANGERED SPECIES WITH STAGE-STRUCTURE AND MIGRATIONS IN POLLUTED ENVIRONMENTS

We propose a stochastic stage-structured single-species model with migrations and hunting within a polluted environment,where the species is separated into two groups:the immature and the mature,which migrates from one patch to another with different migration rates.By constructing a Lyapunov function,together with stochastic analysis approach,the stochastic single-species model admits a unique global positive solution.We then utilize the comparison theorem of stochastic differential equations to investigate the extinction and persistence of solution to stochastic single-species model.The main results indicate that the species densities all depend on the intensities of random perturbations within both patches.As a consequence,we further provide several strategies for protecting endangered species within protected and unprotected patches.