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 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 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 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 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 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 Global Stability of an Epidemic Model with Incomplete Treatment and Vaccination

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hai-Feng Huo ◽  
Li-Xiang Feng
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Incomplete Treatment ◽  
Disease Free ◽  
The Basic Reproduction Number

An epidemic model with incomplete treatment and vaccination for the newborns and susceptibles is constructed. We establish that the global dynamics are completely determined by the basic reproduction numberR0. IfR0≤1, then the disease-free equilibrium is globally asymptotically stable. IfR0>1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also given to explain our conclusions.

scholarly journals Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations

1993 ◽  
Vol 34 (3) ◽  
pp. 282-295 ◽  
Author(s):  
Xiaodong Lin ◽  
Joseph W.-H. So
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Epidemic Models ◽  
Uniform Persistence ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Rates ◽  
Effective Contact

AbstractWe consider the epidemic model with subpopulations introduced in Hethcote [5]. It is shown that if the endemic equilibrium exists, then the system is uniformly persistent. Moreover, the endemic equilibrium is globally asymptotically stable under the assumption of small effective contact rates between different subpopulations.

scholarly journals A mathematical investigation of an "SVEIR" epidemic model for the measles transmission

2022 ◽  
Vol 19 (3) ◽  
pp. 2853-2875
Author(s):  
Miled El Hajji ◽  
◽  
Amer Hassan Albargi ◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Basic Reproduction Number

<abstract><p>A generalized "SVEIR" epidemic model with general nonlinear incidence rate has been proposed as a candidate model for measles virus dynamics. The basic reproduction number $ \mathcal{R} $, an important epidemiologic index, was calculated using the next generation matrix method. The existence and uniqueness of the steady states, namely, disease-free equilibrium ($ \mathcal{E}_0 $) and endemic equilibrium ($ \mathcal{E}_1 $) was studied. Therefore, the local and global stability analysis are carried out. It is proved that $ \mathcal{E}_0 $ is locally asymptotically stable once $ \mathcal{R} $ is less than. However, if $ \mathcal{R} &gt; 1 $ then $ \mathcal{E}_0 $ is unstable. We proved also that $ \mathcal{E}_1 $ is locally asymptotically stable once $ \mathcal{R} &gt; 1 $. The global stability of both equilibrium $ \mathcal{E}_0 $ and $ \mathcal{E}_1 $ is discussed where we proved that $ \mathcal{E}_0 $ is globally asymptotically stable once $ \mathcal{R}\leq 1 $, and $ \mathcal{E}_1 $ is globally asymptotically stable once $ \mathcal{R} &gt; 1 $. The sensitivity analysis of the basic reproduction number $ \mathcal{R} $ with respect to the model parameters is carried out. In a second step, a vaccination strategy related to this model will be considered to optimise the infected and exposed individuals. We formulated a nonlinear optimal control problem and the existence, uniqueness and the characterisation of the optimal solution was discussed. An algorithm inspired from the Gauss-Seidel method was used to resolve the optimal control problem. Some numerical tests was given confirming the obtained theoretical results.</p></abstract>

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 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.

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