Virus Propagation In Networks Research Articles

Analysis of Epidemic Models in Complex Networks and Node Isolation Strategie Proposal for Reducing Virus Propagation

Many models of virus propagation in Computer Networks inspired by epidemic disease propagation mathematical models that can be found in the epidemiology field (SIS, SIR, SIRS, etc.) have been proposed in the last two decades. The purpose of these models has been to determine the conditions under which a virus becomes rapidly extinct in a network. The most common models of virus propagation in networks are SIS-type models or their variants. In such models, the conditions that lead to a rapid extinction of the spread of a computer virus have been calculated and its dependence on some parameters inherent to the mathematical model has been observed. In this article, we will try to analyze a particular SIS-type model proposed in the past by Chakrabarti as well as an SIRS-type variation of this model proposed in the past by myself. I will show through simulations the influence that the topology of a network has on the dynamics of the spread of a virus in different network types. In the recent past, there have been interesting articles that demonstrate the relationship between the eigenvalue λ1 of the adjacency matrix and the reduction in the spread of a virus in a network. From this, the minimization of the spectral radius strategies by edge suppression has been proposed. This problem is NP-complete in its general case and for this reason, heuristic algorithms have been proposed. In this article, I will perform simulations of an SIS-type model in topologies with the same number of nodes but with different structures to compare their epidemic behavior. The simulations will show that regular topologies with small node degrees, i.e., of degree 4, as is the case of the topology that I call Lattice4, have favorable behavior in terms of the fast extinction property, with respect to other denser and less regular topologies such as the binomial topologies as well as Power law topologies. Based on the results of the simulations, my contribution will consist of proposing, as a node isolation strategy, a transformation of the original topology into an approximately regular topology by edge elimination. Although such a transformed topology is not optimal in terms of reducing the propagation of a virus, it induces the rapid extinction of the virus in the network.

Network virus propagation and security situation awareness based on Hidden Markov Model

The security situation of the network is determined by the observation state and hidden state of a complex virus system. To analyze the relationship between the two states and evaluate the trends in the security situation of the system, we construct a new model for security situation awareness based on Hidden Markov Model (HMM). Firstly, the paper examines the impact of virus propagation on network security and proposes a new SIR (Susceptible–Infected–Recovered) virus propagation model on scale-free networks. Secondly, we construct a Hidden Markov Model for network security, and this model designs and utilizes the Forward Algorithm and Viterbi Algorithm to assess the security status of epidemic networks. Finally, we ascertain the effectiveness of the model and algorithms through model examples and simulation experiments. The results show that the proposed algorithm is highly efficient in analyzing the security of virus systems and has great application value in predicting the security trends of networks.

Distributed immune time-delay SEIR-S model for new power system information network virus propagation

The new power system information network has the security problem of computer virus attack, and the study of its transmission mechanism is helpful to discover the law and influence of virus transmission. In this paper, the research method of epidemic theory is introduced, and a new Susceptible-Exposed-Infectious-Recovered-Susceptible(SEIR-S) virus model is proposed. The immune time-delay parameter is introduced to simulate the evolution and mutation of the virus so that nodes immune to the virus can still be re-infected after a certain time interval. At the same time, the immune time of different nodes is different, and the distributed immune time delay is used to enhance the authenticity of the simulated virus transmission; and considering the influence of the scale-free characteristics of the information network, this paper establishes a continuous Markov chain based on time. The transmission process of the virus, and then deduce the theoretical analysis results of the virus infection rate threshold. Based on theoretical analysis, the propagation process of the SEIR-S virus model with distributed immune time delay was simulated by using the Monte Carlo method, and the accuracy of the threshold formula of virus infection rate was verified. The influence rule of the hysteresis parameter, that is, increasing the average immune time of nodes to viruses can reduce the infection density of the network in a steady, and at the same time, making the immune time of network nodes obey a normal distribution can effectively reduce the oscillation effect of viruses on the network.

SLBRS: Network Virus Propagation Model based on Safety Entropy

Network viruses pose a great threat to cyberspace, which makes people study many different models of network virus propagation based on dynamic system theory. However, many models of network virus have not been carried out in-depth analysis on the security situation of network virus system, especially the research on the security of network virus propagation model using safety entropy is still in the early stage. In this paper, we propose a new type of SLBRS (Susceptible–Latent–Breaking-out–Recovered–Susceptible) network virus propagation model. Firstly, we analyze the dynamic characteristics of the SLBRS model such as stability, periodic orbit and basic reproduction number. Secondly, we analyzed the security of SLBRS model, and studied the security trend of the virus system on the basis of safety entropy and its derivative. Finally, numerical simulation experiments were carried out on SLBRS model and the trend of safety entropy, the simulation results verify the correctness of the model. Numerical simulation shows that SLBRS model avoids the shortcomings of state and parameter processing in previous studies, and the SLBRS model can describe the security trend of the system intuitively and effectively by using the method of safety entropy.

A Network Virus Propagation Model with Distributed Infectious Period Delay in Internet

A novel propagation model with distributed infectious period delay of network virus is presented. The formula of basic reproduction number for the model is given. The viruses eventually disappear when the basic reproductive number is below the unity, otherwise the viruses are persistent.

Heterogeneous virus propagation in networks: a theoretical study

The node‐based epidemic modeling is an effective approach to the understanding of the impact of the structure of the propagation network on the epidemics of electronic virus. In view of the heterogeneity of the propagation network, a heterogeneous node‐based SIRS model is proposed. Theoretical analysis shows that the maximum eigenvalue of a matrix related to the model determines whether viruses tend to extinction or persist. When viruses persist, the connectedness of the propagation network implies the existence and uniqueness of a viral equilibrium, and a set of sufficient conditions for the global stability of the viral equilibrium are given. Numerical examples verify the correctness of our results. Copyright © 2016 John Wiley & Sons, Ltd.

一类计算机病毒入侵的数学模型分析

本文研究一类具有标准发生率的SIR网络病毒传播模型，得到病毒入侵失败和成功的阈值及病毒存在情形下的平衡点的稳定性，在此基础上为控制病毒传播提出了一些策略。 This paper studies a network virus propagation SIR model with standard incidence rate. We get the threshold value which shows that when the virus will invade successfully and when it will fail. Further, using the balance theory of ordinary differential equations, we analyze the stability of the equilibrium and give some suggestions to control the spreading of the virus.

On modeling the crowding and psychological effects in network-virus prevalence with nonlinear epidemic model

The fast point-to-group information sharing process within an enterprise network also exposes information to more severe virus attacks. On the other hand, a relative large number of virus attacks may result in psychological effects of inhibition for the network end-users. In this paper, a nonlinear force of infection function for e-SEIR model is presented to study the crowding and psychological effects in network virus prevalence. By carrying out a global analysis of the stability of both the virus-free and endemic equilibrium, this work reveals how the crowding and psychological effects have impacts on network virus propagation process. Furthermore, analysis and simulation results show some managerial insights that are helpful for the practice of antivirus in information sharing networks.

Hopf bifurcation analysis of a delayed viral infection model in computer networks

In this paper, a novel computer virus propagation model with dual delays and multi-state antivirus measures is considered. Using theories of stability and bifurcation, it is proven that there exists a critical value of delay for the stability of virus prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the explicit formulas determining the stability and direction of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to verify the theoretical analysis. The conclusions of this paper can contribute to a better theoretical basis for understanding the long-term actions of virus propagation in networks.

Infection Functions for Virus Propagation in Computer Networks: An Empirical Study

There has been an increasing amount of interest in modeling virus propagation in recent years. However, the group-based infection mechanism of computer viruses is not well understood and the selection of infection function in virus propagation modeling has not been well studied. This paper describes a point-to-group (P2G) infection mode to describe virus propagation in networks with information sharing groups. Simulations compare the constant infection and I-type infection functions with the new E-type infection function in the small-world-network environment. The simulation results show that the E-type infection function shows superior performances to that of the traditional I-type infection function in modeling the P2G virus infection mechanism and the I-type infection function shows better performance in modeling the random infection mechanism.

Towards controlling virus propagation in information systems with point-to-group information sharing

Nowadays, for information systems at organizational and interorganizational levels, information sharing is essential for business operations and strategic decision-making. As a mixed blessing, however, the information sharing process also exposes information systems to more severe virus attacks. In light of this, research efforts on virus propagation and virus control have drawn increasing interests in both the academic and industrial domains. This paper thus presents a virus propagation model, namely E-SEIR, to gain insights of virus propagation in networks with Point-to-Group (P2G) information sharing patterns. Unlike most existing virus propagation models, E-SEIR has three important characteristics. First, an additional exposed state is integrated into the model to describe the latent period of computer viruses. Second, a P2G infection function is introduced to the model to characterize the real-world networks, which consist of many information-sharing sub-networks. Third, E-SEIR takes various antivirus countermeasures into consideration, which provides unique opportunities for studying the behaviors of virus propagation with the presence of antivirus activities. Based on this E-SEIR model, we have studied the possibility of short-term virus outbreaks and long-term network survivability, and the results revealed some key managerial insights that are helpful for the practice of virus propagation control in information sharing networks.

The minimal spectral radius of graphs with a given diameter

The spectral radius of a graph (i.e., the largest eigenvalue of its corresponding adjacency matrix) plays an important role in modeling virus propagation in networks. In fact, the smaller the spectral radius, the larger the robustness of a network against the spread of viruses. Among all connected graphs on n nodes the path P n has minimal spectral radius. However, its diameter D, i.e., the maximum number of hops between any pair of nodes in the graph, is the largest possible, namely D = n − 1. In general, communication networks are designed such that the diameter is small, because the larger the number of nodes traversed on a connection, the lower the quality of the service running over the network. This leads us to state the following problem: which connected graph on n nodes and a given diameter D has minimal spectral radius? In this paper we solve this problem explicitly for graphs with diameter D ∈ 1 , 2 , n 2 , n - 3 , n - 2 , n - 1 . Moreover, we solve the problem for almost all graphs on at most 20 nodes by a computer search.