个体在随机和异质网络相互转化的传染病模型研究

利用将人群分为随机和异质的两个子网,且个体可以在这两个子网之间相互转化的方法,建立了随机和异质接触传播模式不能同时在每个个体身上发生的一类多途径传染病模型.利用极限系统以及Gershgorin圆盘定理证明了模型的无病平衡点的唯一性,并利用下一代矩阵方法计算得到了模型的基本再生数,得到无病平衡点的稳定性,进而得到了在基本再生数小于1时疾病最终消亡的结论.

一类网络上的SIS传染病模型

文章研究了网络上SIS传染病模型,考虑了交叉感染、迁移扩散以及迁移时滞对传染病传播的影响.结合图论中强连通图的相关知识构造出恰当的Lyapunov泛函,证明系统的一致有界性.同时利用强次线性求出了阈值s,给出无病平衡点和地方病平衡的全局渐近稳定的条件.

独立生存的两菌株对逼近模型

建立了两种菌株生存的对逼近模型,研究了两种菌株独立生存和共存的条件.利用雅可比矩阵证明了无病平衡点的局部稳定性,通过矩阵理论分析特征值的相关方法得到了与两菌株相对应的基本再生数的表达式,进而得到边界平衡点及正平衡点存在的条件.最后选取适当的模型参数利用Matlab进行了计算机模拟,验证了边界平衡点及正平衡点的稳定性.

Epidemic Spreading Model Based on Social Active Degree in Social Networks

In this paper,an improved Susceptible-Infected-Susceptible(SIS) epidemic spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases.This model is based on the following ideas:in social networks,the contact probability between nodes is decided by their social distances and their active degrees.The contact probability of two indirectly connected nodes is decided by the shortest path between them.Theoretical analysis and simulation experiment were conducted to evaluate the performance of this improved model.Because the proposed model is independent of the network structure,simulation experiments were done in several kinds of networks,namely the ER network,the random regular network,the WS small world network,and the BA scale-free network,in order to study the influences of certain factors have on the epidemic spreading,such as the social contact active degree,the network structure,the average degree,etc.This improved model provides an idea for studying the spreading rule of computer virus,attitudes,fashion styles and public opinions in social networks.

Modeling of Malicious Code Propagations in Internet of Things

Nowadays, the main communication object of Internet is human-human. But it is foreseeable that in the near future any object will have a unique identification and can be addressed and con- nected. The Internet will expand to the Internet of Things. IPv6 is the cornerstone of the Internet of Things. In this paper, we investigate a fast active worm, referred to as topological worm, which can propagate twice to more than three times faster tl^an a traditional scan-based worm. Topological worm spreads over AS-level network topology, making traditional epidemic models invalid for modeling the propagation of it. For this reason, we study topological worm propagation relying on simulations. First, we propose a new complex weighted network mod- el, which represents the real IPv6 AS-level network topology. And then, a new worm propagation model based on the weighted network model is constructed, which descries the topological worm propagation over AS-level network topology. The simulation results verify the topological worm model and demonstrate the effect of parameters on the propagation.

Steady States in SIRS Epidemical Model of Mobile Individual

We consider an epidemical model within soclally interacting mobile individuals to study the behaviors of steady states of epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds δc and pc below which infectious disease dies out. For the population density δ far above δc it is found that there is linear relationship between contact rate λ and the population density δ in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.

SEIR Model of Rumor Spreading in Online Social Network with Varying Total Population Size

Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.

Threshold analysis for epidemic models with high-risk immunization on networks

In this paper, an SIRS epidemic model with high-risk immunization was investigated, where a susceptible neighbor of an infected node is immunized with rate h. Through analyzing the discrete-time model, we found that the epidemic threshold above which an epidemic can prevail and persist in a population is inversely proportional to 1 - h value. We also studied the continuous-time epidemic model and obtained a different result： the epidemic threshold does not depend on the immunization parameter h. Our results suggest that the difference between the discrete-time epidemic model and the continuous-time epidemic model exists in the high-risk immunization.

Network and equation-based models in epidemiology

Network and equation-based （EB） models are two prominent methods used in the study of epidemics. While EB models use a global approach to model aggregate population, net- work models focus on the behavior of individuals in the population. The two approaches have been used in several areas of research, including finance, computer science, social science and epidemiology. In this study, epidemiology is used to contrast EB models with network models. The methods are based on the assumptions and properties of compartmental models. In EB models we solve a system of ordinary differential equations and in network models we simulate the spread of epidemics on contact networks using bond percolation. We examine the impact of network structures on the spread of infection by considering various networks, including Poisson, Erd3s R6nyi, Scale-free, and Watts- Strogatz small-world networks, and discuss how control measures can make use of the network structures. In addition, we simulate EB assumptions on Watts-Strogatz net- works to determine when the results are similar to that of EB models. As a case study, we use data from the 1918 Spanish flu pandemic and that from measles outbreak to validate our results.

Dynamic analysis of an SEIRS model with nonlinear infectivity on complex networks

In this paper, we study the spreading of infections on complex heterogeneous networks based on an SEIRS epidemic model with nonlinear infectivity. By mathematical analysis, the basic reproduction number R0 is obtained. When R0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R0 is greater than one, the disease-free equilibrium becomes unstable and the disease is permanent, and in the meantime there exists a unique endemic equilibrium which is globally attrac- tive under certain conditions. Finally, the effects of various immunization schemes are studied. To verify our theoretical results, the corresponding numerical simulations are also included.