Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model

In the new social media era, it is becoming increasingly important to explore the propagation rules for rumors in social networks. This article is concerned with investigating a diffusive susceptible-infected rumor propagation model with a nonlinear propagation function in a spatially heterogeneous environment. We establish the uniform persistence and analyze the asymptotic behavior of the rumor-spreading steady state for the spatially heterogeneous model when one of the diffusion coefficients tends to zero. Moreover, to better reflect the effect of a time delay on the process of rumor propagation, we establish a spatially homogeneous model with a time delay and prove the existence and local stability of the corresponding equilibrium point. Furthermore, the optimal control in the spatially homogeneous environment case is derived. Finally, several numerical simulations are performed to verify the theoretical results in both spatially heterogeneous and spatially homogeneous systems.     

The stochastic evolution of rumors within a population

We study rumor propagation process with incubation and constant immigration. We take into account a deterministic rumor spreading model and demonstrate the persistence of a rumor when the basic reproduction number is greater than one. Due to the presence of a randomness in the influence that the incubators exert on ignorants, we extrapolate the deterministic rumor model to a stochastic one by using a stochastic coefficient for the term representing the latter influence within the system. The existence and boundedness of both local and global solutions are demonstrated. We prove the uniqueness of these solutions. Conditions of extinction is also established. We perform numerical simulations to verify our stochastic model. The present work can assist decision takers in the analysis of the dynamical evolution of rumors in a given society as well as in the study of information dissemination strategies.     

Dynamic analysis of a rumor propagation model with Lévy noise

In this paper, we are concerned with a rumor propagation model with L vy noise. We first prove that there exists a positive global solution. Then, the asymptotic behaviors around the rumor‐free equilibrium and rumor‐epidemic equilibrium are obtained. Lastly, simulations verify our results.     

Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

     

考虑媒体播报效应的双时滞传染病模型

在疾病控制过程中, 媒体的重要性举足轻重.该文旨在建立并分析一个含有媒体效应的多时滞传染病模型, 研究模型的稳定性, 并通过分析相应特征方程根, 分别研究在时滞不同的5种情况下, 系统的稳定性发生变化, 以及产生Hopf分支的条件.再利用持续性理论, 证明模型的持续生存性.最后将时滞模型研究结果应用于苏格兰小儿肺炎中, 验证媒体效应对疫情控制起到的重要作用以及时滞大小对模型稳定性的影响.     

流体饱和多孔介质中波传播问题的有限元分析

采用基于混合物理论的多孔介质模型,给出流体饱和两相多孔介质波动问题的有限元分析方法·　采用罚方法导出的有限元动力方程,时间积分可采用显式和隐式积分两种方案·　用编制的有限元程序分析了一维柱体在跃阶载荷和脉冲载荷作用下的波传播问题,得到该两种瞬态载荷作用下固体和流体相位移、速度以及固体相有效应力和孔隙压力随时间的变化关系,并对波的传播现象进行了分析·　所得结果与理论相吻合·     

考虑公众风险感知的突发事件风险传播模型及仿真研究

突发事件应对过程中,公众对突发事件的风险感知会在一定程度上决定其行为选择从而影响事件风险的传播。为此,本文通过分析突发事件风险信息、风险感知和风险传播的路径关系,在风险传播过程中引入传染病传播机制,构建基于微分方程的风险传播模型。综合考虑风险传播阈值、媒体报道力度、群体风险感知度、个人风险知识水平四类因素并结合仿真实验分析对风险感知和风险传播行为的影响。最后,通过实例研究表明模型结论的有效性。本文研究结论有助于为相关职能部门调节公众风险感知,制定风险防控措施提供理论依据与支持。     

Analysis of a stochastic recovery-relapse epidemic model with periodic parameters and media coverage

This paper addresses, motivated by mathematical work on infectious disease models, the impacts of environmental noise and media coverage on the dynamics of recovery-relapse infectious diseases. A susceptible-infectious-recovered-infectious model is formulated with both vertical transmission and horizontal transmission. The existence and uniqueness of the positive global solution is studied by constructing suitable Lyapunov-type function. Then, the existence of positive periodic solutions is verified by applying Khasminskii"s theory. The existence of positive periodic solutions indicates the continued survival of the diseases. Besides, sufficient conditions for the extinction of the diseases are obtained. Numerical simulations then demonstrate the dynamics of the solutions. The paper extends the results of the corresponding deterministic system.     

Lévy noise perturbation for an epidemic model with impact of media coverage

ABSTRACT

This work is devoted to study the existence and uniqueness of global positive solution for a stochastic epidemic model with media coverage driven by Lévy noise. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Numerical simulations are presented to confirm the theoretical results.     

An Infectious Disease Model With Media Coverage and Limited Medical Resources北大核心CSCD

该文建立和分析了一类具有媒体报道效应和有限医疗资源的传染病动力学模型,定义了疾病的基本再生数,分析了平衡点的存在性和稳定性,给出了系统发生前向分支、后向分支和Hopf分支的条件.通过数值模拟发现：提高媒体报道的信息覆盖率或医院对病人的最大容纳量,可以显著降低疾病流行的峰值或稳态时的感染人数;随着参数变化,系统不仅可能会产生后向分支或前向分支,还可能会出现鞍结点分支、Hopf分支以及地方病平衡点稳定性随参数变化而变化等动力学行为.     

Models of unidirectional propagation in heterogeneous excitable media

Two differential equation models of excitable media (threshold and recovery kinetics) with solutions that exhibit unidirectional propagation are presented. It is shown that unidirectional propagation in heterogeneous excitable media with non-oscillatory kinetics can be initiated from homogeneous initial data. Simulations on a reaction-diffusion model with FitzHugh-Nagumo kinetics and spatially heterogeneous parameters yields a rotating wave on a one-dimensional circular spatial domain. An ordinary differential equation model with four semi-coupled excitable cells and heterogeneous parameters is analyzed to determine a critical parameter region over which unidirectional propagation may occur.     

高速冲击条件下玻璃中破坏波的损伤累积模拟

分析了玻璃介质在高速冲击条件下低于Hugoniot应力弹性极限时的破坏波现象,在实验现象分析的基础上提出了一种由偏应力冲量决定的损伤累积模型,模型中采用了Heaviside函数来描述材料内部的破坏延迟现象,分析了玻璃介质中破坏层的性质、破坏波的传播机制及其动态特征,并发现了反射稀疏波在破坏层边界再次反射后破坏波传播速度下降的现象。     

An initial boundary-value problem for model electromagnetoelasticity system

In this paper we consider an initial boundary-value problem related to the electrodynamics of vibrating elastic media. The aim is to prove an existence and uniqueness result for a model describing the nonlinear interactions of the electromagnetic and elastic waves. We assume that the motion of the continuum occurs at velocities that are much smaller than the propagation velocity of the electromagnetic waves through the elastic medium. The model under study consists of two coupled differential equations, one of them is the hyperbolic equation (an analog of the Lamé system) and another one is the parabolic equation (an analog of the diffusion Maxwell system). One stability result is proved too.     

Smoothed Particle Hydrodynamics modelling of poroelastic media

Numerical modelling of poroelastic properties in porous media allows widely varied investigations at low costs and relatively short times. The study of porous media is of high interest at different scales, in this case we focus our analysis at meso- and macroscale which is highly relevant e.g. in geothermal explorations. We model a biphasic poroelastic media assuming incompressible fluid and solid grains and a large solid-fluid density ratio. Meshfree methods are nowadays more widely used due to the advantages that present in the simulation of large deformations. In this case we choose to employ the Smoothed Particle Hydrodynamics method (SPH), a Lagrangian method where the domain is discretized in particles. The solution is computed in parallel, which allows to simulate large domains more representative of the scale of our study cases. We validate our implementation with a classical consolidation problem and compare the simulated diffusion process with Terzaghi's analytical solution. Future work includes simulation of fractures initiation and propagation in the porous media at reservoir scale. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of information epidemics modeled as Maki Thompson rumors

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin’s Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas.We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns.     

Long-Time Behavior of the Mean Curvature Flow with Periodic Forcing

We consider the long-time behavior of the mean curvature flow in heterogeneous media with periodic fibrations, modeled as an additive driving force. Under appropriate assumptions on the forcing term, we show existence of generalized traveling waves with maximal speed of propagation, and we prove the convergence of solutions to the forced mean curvature flow to these generalized waves.     

Threshold of damped critical non-linear Schrödinger equation with fourth-order dispersion

This article is concerned with a damped critical non-linear Schrödinger equation with fourth-order dispersion which models propagation of fibre arrays in non-linear Kerr media. We analyse the effect of the damping force on the solution for the system and prove that there exists a threshold value of the damping parameter for global existence and blowup of the system. Furthermore, we estimate the threshold value.     

Global attractors for von Karman evolutions with a nonlinear boundary dissipation

Dynamic von Karman equations with a nonlinear boundary dissipation are considered. Questions related to long time behaviour, existence and structure of global attractors are studied. It is shown that a nonlinear boundary dissipation with a large damping parameter leads to an existence of global (compact) attractor for all weak (finite energy) solutions. This result has been known in the case of full interior dissipation, but it is new in the case when the boundary damping is the main dissipative mechanism in the system. In addition, we prove that fractal dimension of the attractor is finite. The proofs depend critically on the infinite speed of propagation associated with the von Karman model considered.     

Nonstationary love waves of the SH-type in an anisotropic elastic medium. A kinematic approach

In this paper, the propagation of Love waves in anisotropic elastic media is studied. These waves are a similar to the transverse surface SH waves in the isotropic case. Necessary conditions for the existence of Love waves of this polarization type near the surface Σ of an anisotropic elastic body are deduced. The algorithm developed here makes it possible to find the direction (s) of transverse surface wave propagation (at every point on the surface Σ). The algorithm employed is illustrated by some special anisotropic cases. The space-time method is used to construct the asymptotics of Love waves for those types of anisotropic media the eikonal equation of which is valid on the surface of an elastic body. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 262–276 Translated by Z. A. Yanson