A Reliable numerical scheme for a computer virus propagation model

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.

GLOBAL DYNAMICS OF A COMPUTER VIRUS PROPAGATION MODEL WITH FEEDBACK CONTROLS

A computer virus propagation model with feedback controls is first proposed and investigated. We show that the control variables do not influence on the global stability of the original differential model, they only alter the position of the unique viral equilibrium. The mathematical analyses and numerical simulations show that this equilibrium can be completely eliminated, namely, moved to the origin of coordinates if suitable values of the control variables are chosen. In the other words, the control variables are effective in the prevention of viruses in computer systems. Some numerical simulations are presented to demonstrate the validity of the obtained theoretical results.

Global Behavior of a Computer Virus Propagation Model on Multilayer Networks

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.

Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate

A four-compartment computer virus propagation model with two delays and graded infection rate is investigated in this paper. The critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation. In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results.