An SLBRS Model with Vertical Transmission of Computer Virus over the Internet

Abstract

By incorporating an additional recovery compartment in the SLBS model, a new model, known as the SLBRS model, is proposed in this paper. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a thresholdℛ0. Specially, virus-free equilibrium is globally asymptotically stable ifℛ0≤1, whereas the viral equilibrium is globally asymptotically stable ifℛ0>1. Next, the sensitivity analysis ofℛ0to four system parameters is also analyzed. On this basis, a collection of strategies are advised for eradicating viruses spreading across the Internet effectively.

Towards Modeling Malicious Agents in Decentralized Wireless Sensor Networks: A Case of Vertical Worm Transmissions and Containment

“…Li, et al [12] employed the parameters for vertical transmission for the global dynamical analysis of disease models and [11] extended it to computer networks where the worm infection is seen to pass from the main server to any node using the Susceptible-Exposed-Infectious-Recovered (SEIR) model. There exists other works that investigated the vertical transmission in computer networks using the Susceptible-Latent-Breaking Out-Susceptible (SLBS) [13] and the Susceptible-Latent-Breaking Out-RemovedSusceptible (SLBRS) [14]. To the best of our knowledge it has not been applied for the study of worm dynamics in WSNs.…”

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

“…This is inconsistent with the fact that an infected computer which is in latency can also infect other computers through file copying or file downloading. Based on this, Yang et al proposed some models [14][15][16][17], by taking into account the fact that a computer immediately possesses infectivity once it is infected. However, these models make an assumption that the exposed computers and the infectious computers have the same infectivity.…”

Modeling the Spread of Computer Viruses under the Effects of Infected External Computers and Removable Storage Media

“…In order to remedy this flaw, Yang et al [14] proposed a three-compartment model for computer viruses which is known as the original SLBS (susceptible-latent-breaking-susceptible) model. By incorporating a called R (recovered)-compartment into the SLBS model, Yang et al [15] proposed a fourcompartment model which is known as the original SLBRS (susceptible-latent-breakingrecovered-susceptible) model. Subsequently, in order to investigate the impact of infected external computers (i.e., a computer outside the Internet) on viral spread and based on the original SLBRS model, a dynamical model [16] has been proposed.…”