scholarly journals A Reliable numerical scheme for a computer virus propagation model

2021 ◽  
Author(s):  
Hoai Thu Pham ◽  
Manh Tuan Hoang
Keyword(s):  
Numerical Experiments ◽  
Numerical Scheme ◽  
Computer Virus ◽  
Propagation Model ◽  
Virus Propagation ◽  
Essential Properties ◽  
Computer Virus Propagation Model ◽  
Nsfd Scheme ◽  
Theoretical Results ◽  
Good Agreement

In this paper, we apply the Mickens’methodology to construct a dynamically consistentnonstandard finite difference (NSFD) scheme for acomputer virus propagation model. It is proved thatthe constructed NSFD scheme correctly preservesessential mathematical features of the continuous-timemodel, which are positivity, boundedness and asymptotic stability. Consequently, we obtain an effectivenumerical scheme that can provide reliable approximations for the computer virus propagation model.Meanwhile, some typical standard finite differenceschemes fail to preserve the essential properties ofthe computer virus propagation model; hence, theycan generate numerical approximations which arenot only negative but also unstable. Finally, a setof numerical experiments is performed to supportthe theoretical results as well as to demonstrate theadvantage of the NSFD scheme over standard ones.As we expected, there is a good agreement betweenthe numerical results and theoretical assertions.

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.

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.

A novel computer virus propagation model and its dynamics

2012 ◽  
Vol 89 (17) ◽  
pp. 2307-2314 ◽  
Author(s):  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Luosheng Wen ◽  
Jiming Liu
Keyword(s):  
Computer Virus ◽  
Propagation Model ◽  
Virus Propagation ◽  
Computer Virus Propagation Model
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