Stability Analysis of a Quarantined Epidemic Model with Latent and Breaking-Out over the Internet

Abstract

In this paper, a new epidemic model, known as the SLBQRS model, is proposed in a computer network with Latent and Breaking-out periods of a virus in its life cycle. Furthermore, an infected computer will be referred to as latent or breaking-out depending on whether all viruses staying in it are in their respective latent periods or at least one virus staying in it is in its breaking-out period. In the real world there exists no infected computer at all that has no infectivity. A breaking-out computer can get treated with a higher probability, because it usually suffers from a marked performance degradation or even breaks down, which can be perceived evidently by the user. The quarantine is a method of isolating the most infected nodes from the network and reduce the spreading virus till they get recovered. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a threshold R 0. Specially, virus-free equilibrium is globally asymptotically stable if R 0 ≤ 1. Next, the sensitivity analysis of R 0 to six system parameters is also analyzed. On this basis, a collection of strategies are advised for eradicating viruses spreading across the Internet effectively. Threshold R 0 , equilibrium and their stability are discussed in terms of the Jacobian of the system. Numerical methods and MATLAB are employed to solve and simulate the system of equations developed and analysis of the model gives remarkable exposure.

Numerical modeling of susceptible latent breaking-out quarantine computer virus epidemic dynamics

“…The system of nonlinear differential equations for SLBQRS epidemic model [1] is given as with initial conditions …”

“…It can also transmit by downloading any file from internet, network connections, floppy disk, and universal serial buses or by CDs. To study the prevention and control of the spread of virus in computers, epidemic models for computer virus dynamics are established in recent years [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. The spread of virus can be controlled by isolating the highly infected nodes.…”

“…In this work, we solved numerically the quarantined epidemic model with latent and breaking-out over the internet [1] . The term latent is referred for the infected computers with latent period to become infectious.…”

Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software

“…However, as stated in [20], those above models with the exposed compartment neglect the fact that a computer can infect other computers through file copying or file downloading. Therefore, to overcome the above-mentioned defect, computer virus models with infectivity in latent period have received much attention in recent years [21][22][23][24][25][26]. Unfortunately, most of these models still have some defects.…”

The Impact of Quarantine Strategies on Malware Dynamics in a Network With Heterogeneous Immunity

“…In [8], two compartments, the latent and the breakout computers, were introduced into the quarantine dynamics of computer viruses (SLBQRS). Moreover, they assumed that latent computers posses infectivity, unlike other models with latent class; as a result, computers are infected due to contact with infected computers from the latent or the breakout compartments.…”