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In this paper, a model with two different frameworks of an attacking class and a targeted class is introduced to study the virus mobility of an attack in a targeted network. Existence and stability of equilibrium points are discussed in equivalence with the basic reproduction number R 0. It is observed that as R 0 crosses unity, transcritical bifurcation arises in the system. The effect of firewall security is also shown graphically which has been taken as a media coverage factor in this work and it is discovered that firewall helps to bring down the virus propagation by reducing the infection peak. Optimal control concept is then introduced to propose one more measure for regulating the virus propagation. Numerical experimentations have been done to rationalize the analytical conclusions. In the end, a sensitivity analysis is executed that provides the information about relevance of parameters in deciding the virus spread in networks. • A new model governing DDoS attacks has been proposed to study the virus mobility in targeted network. • Firewall helps to control virus proliferation to a symbolic level by lowering the infection level. • Optimal control theory has been proposed as one more measure for regulating the virus propagation. • Sensitivity analysis is executed that provides information about the virus spread in networks. [ABSTRACT FROM AUTHOR]

We propose an e-epidemic time-delay Susceptible-Latent-Breaking out-Susceptible (S L B S ) model to study delay dynamics appearing due to antivirus software, which takes time to clean the viruses from latent and breaking-out computers. We perform nonlinear stability analysis, Hopf bifurcation analysis, and its direction and stability. Numerical simulation results (time series analysis and bifurcation diagram) give useful insights for delay dynamics. We investigate the effect of the control parameters like rate of infection of all the classes and cure rates on the model system. Our results suggest that time delay is responsible for destabilizing the system dynamics. For smooth functionality of a computer system, our results suggest the minimum use of removable storage devices like smart phones, optical discs, memory cards, external hard disk, digital cameras, and so on and use of effective antivirus softwares. [ABSTRACT FROM AUTHOR]

We are concerned with the Hopf bifurcation of an SVEIR computer virus model with time delay and nonlinear incident rate. First of all, by analyzing the associated characteristic equation we obtain sufficient conditions for its local stability and the existence of a Hopf bifurcation. Directly afterward, by means of the normal form theory and the center manifold theorem we derive explicit formulas that determine the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions. Finally, we carry out numerical simulations to illustrate and verify the theoretical results. [ABSTRACT FROM AUTHOR]