scholarly journals Propagation Behavior of Virus Codes in the Situation That Infected Computers Are Connected to the Internet with Positive Probability

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lu-Xing Yang ◽  
Xiaofan Yang
Keyword(s):  
Theoretical Analysis ◽  
Threshold Value ◽  
Computer Virus ◽  
The Internet ◽  
Asymptotically Stable ◽  
Positive Probability ◽  
Globally Asymptotically Stable ◽  
New Model ◽  
Propagation Behavior ◽  
Viral Equilibrium

All the known models describing the propagation of virus codes were based on the assumption that a computer is uninfected at the time it is being connected to the Internet. In reality, however, it is much likely that infected computers are connected to the Internet. This paper is intended to investigate the propagation behavior of virus programs provided infected computers are connected to the Internet with positive probability. For that purpose, a new model characterizing the spread of computer virus is proposed. Theoretical analysis of this model indicates that (1) there is a unique (viral) equilibrium, and (2) this equilibrium is globally asymptotically stable. Further study shows that, by taking active measures, the percentage of infected computers can be made below an acceptable threshold value.

scholarly journals An SLBRS Model with Vertical Transmission of Computer Virus over the Internet

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Maobin Yang ◽  
Zhufan Zhang ◽  
Qiang Li ◽  
Gang Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Behavior ◽  
Vertical Transmission ◽  
Computer Virus ◽  
The Internet ◽  
Asymptotically Stable ◽  
Qualitative Properties ◽  
Globally Asymptotically Stable ◽  
New Model ◽  
System Parameters

By incorporating an additional recovery compartment in the SLBS model, a new model, known as the SLBRS model, is proposed in this paper. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a thresholdℛ0. Specially, virus-free equilibrium is globally asymptotically stable ifℛ0≤1, whereas the viral equilibrium is globally asymptotically stable ifℛ0>1. Next, the sensitivity analysis ofℛ0to four system parameters is also analyzed. On this basis, a collection of strategies are advised for eradicating viruses spreading across the Internet effectively.

scholarly journals Propagation of Computer Virus under Human Intervention: A Dynamical Model

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Chenquan Gan ◽  
Xiaofan Yang ◽  
Wanping Liu ◽  
Qingyi Zhu ◽  
Xulong Zhang
Keyword(s):  
Reproduction Number ◽  
Computer Virus ◽  
Parameter Analysis ◽  
Dynamical Model ◽  
The Internet ◽  
Asymptotically Stable ◽  
Human Intervention ◽  
Globally Asymptotically Stable ◽  
Propagation Behavior ◽  
The Basic Reproduction Number

This paper examines the propagation behavior of computer virus under human intervention. A dynamical model describing the spread of computer virus, under which a susceptible computer can become recovered directly and an infected computer can become susceptible directly, is proposed. Through a qualitative analysis of this model, it is found that the virus-free equilibrium is globally asymptotically stable when the basic reproduction numberR0≤1, whereas the viral equilibrium is globally asymptotically stable ifR0>1. Based on these results and a parameter analysis, some appropriate measures for eradicating the spread of computer virus across the Internet are recommended.

scholarly journals Modelling and Analysis of Propagation Behavior of Computer Viruses with Nonlinear Countermeasure Probability and Infected Removable Storage Media

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xulong Zhang ◽  
Yong Li
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Computer Virus ◽  
Dynamical Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Computer Viruses ◽  
Viral Spread ◽  
Propagation Behavior ◽  
Storage Media

The dissemination of countermeasures is diffusely recognized as one of the most valid strategies of containing computer virus diffusion. In order to better understand the impacts of countermeasure and removable storage media on viral spread, this paper addresses a dynamical model, which incorporates nonlinear countermeasure probability and infected removable storage media. Theoretical analysis reveals that the unique (viral) equilibrium of the model is globally asymptotically stable. This main result is also illustrated by some numerical experiments. Additionally, the numerical experiments of different countermeasure probabilities are conducted.

scholarly journals Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Threshold Value ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Virus Propagation ◽  
Globally Asymptotically Stable ◽  
Existence And Stability ◽  
Computer Virus Propagation Model

A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold valueR0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable ifR0<1, whereas the virus equilibrium is globally asymptotically stable ifR0>1. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.

scholarly journals Global Stability of an Epidemic Model of Computer Virus

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaofan Yang ◽  
Bei Liu ◽  
Chenquan Gan
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Computer Virus ◽  
Propagation Model ◽  
Parameter Analysis ◽  
The Internet ◽  
Asymptotically Stable ◽  
Unique Equilibrium ◽  
Globally Asymptotically Stable ◽  
Computer Viruses

With the rapid popularization of the Internet, computers can enter or leave the Internet increasingly frequently. In fact, no antivirus software can detect and remove all sorts of computer viruses. This implies that viruses would persist on the Internet. To better understand the spread of computer viruses in these situations, a new propagation model is established and analyzed. The unique equilibrium of the model is globally asymptotically stable, in accordance with the reality. A parameter analysis of the equilibrium is also conducted.

scholarly journals A New Model for Capturing the Spread of Computer Viruses on Complex-Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chunming Zhang ◽  
Tianliang Feng ◽  
Yun Zhao ◽  
Guifeng Jiang
Keyword(s):  
Computer Virus ◽  
Propagation Model ◽  
Asymptotically Stable ◽  
Virus Propagation ◽  
Systematic Analysis ◽  
Globally Asymptotically Stable ◽  
Computer Viruses ◽  
New Model ◽  
Globally Attractive ◽  
Computer Virus Propagation Model

Based on complex network, this paper proposes a novel computer virus propagation model which is motivated by the traditional SEIRQ model. A systematic analysis of this new model shows that the virus-free equilibrium is globally asymptotically stable when its basic reproduction is less than one, and the viral equilibrium is globally attractive when the basic reproduction is greater than one. Some numerical simulations are finally given to illustrate the main results, implying that these results are applicable to depict the dynamics of virus propagation.

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

scholarly journals Adaptive 3D Distance-Based Formation Control of Multiagent Systems with Unknown Leader Velocity and Coplanar Initial Positions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xuejing Lan ◽  
Wenbiao Xu ◽  
Yun-Shan Wei
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Relative Position ◽  
Formation Control ◽  
Control Law ◽  
Asymptotically Stable ◽  
Coordinate Systems ◽  
Lyapunov Theorem ◽  
Globally Asymptotically Stable ◽  
3 Dimensional

This paper considers the distributed 3-dimensional (3D) distance-based formation control of multiagent systems, where the agents are connected based on an acyclic minimally structural persistent (AMSP) graph. A parameter is designed according to the desired formation shape and is used to solve the problem that there are two formation shapes satisfying the same distance requirements. The unknown moving velocity of the leader agent is estimated adaptively by the followers requiring only the relative position measurements with respect to their local coordinate systems. In addition, the proposed formation controller provides a new way for the agent to leave the initial coplanar location. The 3D formation control law is globally asymptotically stable and has been demonstrated based on the Lyapunov theorem. Finally, two numerical simulations are presented to support the theoretical analysis.

Stability of a CD4+ T cell viral infection model with diffusion

2018 ◽  
Vol 11 (05) ◽  
pp. 1850071 ◽  
Author(s):  
Zhiting Xu ◽  
Youqing Xu
Keyword(s):  
T Cell ◽  
Viral Infection ◽  
Lyapunov Functions ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Viral Infection Model

This paper is devoted to the study of the stability of a CD[Formula: see text] T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value [Formula: see text]; the endemic equilibrium is globally asymptotically stable if [Formula: see text] and [Formula: see text]. Finally, we give an application and numerical simulations to illustrate the main results.

Dynamical Behaviors of a Pest Epidemic Model with Impulsive Control Over a Patchy Environment

2018 ◽  
Vol 28 (14) ◽  
pp. 1850173 ◽  
Author(s):  
Zhichun Yang ◽  
Cheng Chen ◽  
Lanzhu Zhang ◽  
Tingwen Huang
Keyword(s):  
Epidemic Model ◽  
Impulsive Control ◽  
Threshold Value ◽  
Impulsive System ◽  
Asymptotically Stable ◽  
Patchy Environment ◽  
Globally Asymptotically Stable ◽  
Dynamical Behaviors ◽  
Persistence Theory ◽  
Chaotic Characteristic

An epidemic model for pest management with impulsive control over a patchy environment is proposed in this paper. We investigate the dynamical behaviors on extinction and permanence and obtain the threshold value [Formula: see text] of dynamics for the impulsive system by utilizing a small amplitude perturbation method, matrix spectral analysis and persistence theory. We prove that the periodic pest-eradication solution of the system is globally asymptotically stable if [Formula: see text], while the system is persistent if [Formula: see text]. Furthermore, by discussion on the two-patch case, we analyze the effects of the dispersal and impulsive control on dynamical behaviors of the system. Some numerical examples are given to illustrate the effectiveness of the obtained results and to demonstrate the complexity such as chaotic characteristic of the system.

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