scholarly journals Optimal Control of a Delay-Varying Computer Virus Propagation Model

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu ◽  
Chunming Zhang
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Latency Period ◽  
Computer Virus ◽  
Propagation Model ◽  
Optimal Control Strategy ◽  
Virus Propagation ◽  
Virus Model ◽  
Novel Model ◽  
Computer Virus Propagation Model

By incorporating the objective of keeping a low number of infected nodes and a high number of recovered nodes at a lower cost into a known computer virus model (the delay-varying SIRC model) extended by introducing quarantine, a novel model is described by means of the optimal control strategy and theoretically analyzed. Through the comparison of simulation results, it is shown that the propagation of computer virus with varying latency period can be suppressed effectively by the optimal control strategy.

scholarly journals Dynamics of a Delay-Varying Computer Virus Propagation Model

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu ◽  
Yongchang Zhang ◽  
Yongquan Dong ◽  
Guosheng Hao
Keyword(s):  
Lyapunov Method ◽  
Latency Period ◽  
Geometric Approach ◽  
Threshold Value ◽  
Computer Virus ◽  
Propagation Model ◽  
Direct Lyapunov Method ◽  
Virus Propagation ◽  
Novel Model ◽  
Computer Virus Propagation Model

By considering the varying latency period of computer virus, we propose a novel model for computer virus propagation in network. Under this model, we give the threshold value determining whether or not the virus finally dies out, and study the local stability of the virus-free and virus equilibrium. It is found that the model may undergo a Hopf bifurcation. Next, we use different methods to prove the global asymptotic stability of the equilibria: the virus-free equilibrium by using the direct Lyapunov method and virus equilibrium by using a geometric approach. Finally, some numerical examples are given to support our conclusions.

scholarly journals Global Behavior of a Computer Virus Propagation Model on Multilayer Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chunming Zhang
Keyword(s):  
Theoretical Analysis ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Behavior ◽  
Sufficient Condition ◽  
Multilayer Networks ◽  
Virus Propagation ◽  
Simulation Results ◽  
Computer Virus Propagation Model ◽  
Vital Factor

This paper presents a new linear computer viruses propagation model on multilayer networks to explore the mechanism of computer virus propagation. Theoretical analysis demonstrates that the maximum eigenvalue of the sum of all the subnetworks is a vital factor in determining the viral prevalence. And then, a new sufficient condition for the global stability of virus-free equilibrium has been obtained. The persistence of computer virus propagation system has also been proved. Eventually, some numerical simulation results verify the main conclusions of the theoretical analysis.

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 Bifurcation of a Novel Computer Virus Propagation Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu ◽  
Jiming Liu
Keyword(s):  
Global Bifurcation ◽  
Computer Virus ◽  
Propagation Model ◽  
Virus Spread ◽  
Virus Propagation ◽  
Virus Prevalence ◽  
Parameter Values ◽  
First Time ◽  
Computer Virus Propagation Model ◽  
Theoretical Results

In a recent paper by J. Ren et al. (2012), a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.

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