Abstract
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.
Highlights
With the rapid developments of information and communication technologies, computer has brought great convenience to our life
A number of computer virus propagation models, ranging from conventional SIR compartment model [1,2,3] to its extensions [4,5,6,7,8,9,10,11,12,13,14,15,16], were proposed by borrowing from classical epidemic models to investigate the behaviors of computer virus propagation over network
Recently proposed models can distinguish latent computers from infected ones by introducing the L and B compartments [17,18,19], named as the S(susceptible)-L(latent)-B(breaking-out)S(susceptible) model, which represents the dynamics of virus by systems of ordinary differential equations
Summary
With the rapid developments of information and communication technologies, computer has brought great convenience to our life. When attempting to model computer virus propagation, some of characteristics of viruses and networks should be taken into consideration. The aim is to extend and analyze the SLBS computer virus propagation model without delay and incomplete antivirus ability first proposed by Yang et al [17,18,19]. This study is motivated by the fact that the delay plays a key role and is inevitably a complex impact on the investigation of computer virus spreading behaviors [21]. The incorporation of the delay and incomplete antivirus ability of networks makes the model more realistic but its mathematical qualitative analysis may be difficult.
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