Numerical dynamics of nonstandard finite difference schemes for a computer virus propagation model

2019 ◽  
Vol 8 (3) ◽  
pp. 772-778 ◽  
Author(s):  
Quang A. Dang ◽  
Manh Tuan Hoang
Keyword(s):  
Finite Difference ◽  
Computer Virus ◽  
Difference Schemes ◽  
Propagation Model ◽  
Finite Difference Schemes ◽  
Virus Propagation ◽  
Computer Virus Propagation Model ◽  
Nonstandard Finite Difference ◽  
Numerical Dynamics

scholarly journals NONSTANDARD FINITE DIFFERENCE SCHEMES FOR SOLVING A MODIFIED EPIDEMIOLOGICAL MODEL FOR COMPUTER VIRUSES

2018 ◽  
Vol 34 (2) ◽  
pp. 171-185 ◽  
Author(s):  
Tuan Manh Hoang ◽  
A Quang Dang ◽  
Long Quang Dang
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Fourth Order ◽  
Continuous Model ◽  
Propagation Model ◽  
Finite Difference Schemes ◽  
Virus Propagation ◽  
Order Of Accuracy ◽  
Essential Properties ◽  
Nonstandard Finite Difference

In this paper we construct two families of nonstandard finite difference (NSFD) schemes preserving the essential properties of a computer virus propagation model, such as positivity, boundedness and stability. The first family of NSFD schemes is constructed based on the nonlocal discretization and has first order of accuracy, while the second one is based on the combination of a classical Runge-Kutta method and selection of a nonstandard denominator function and it is of fourth order of accuracy. The theoretical study of these families of NSFD schemes is performed with support of numerical simulations. The numerical simulations confirm the accuracy and the efficiency of the fourth order NSFD schemes. They hint that the disease-free equilibrium point is not only locally stable but also globally stable, and then this fact is proved theoretically. The experimental results also show that the global stability of the continuous model is preserved.

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.

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