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Mathematical Problems in Engineering
Volume 2012, Article ID 407064, 13 pages
http://dx.doi.org/10.1155/2012/407064
Research Article

Two Quarantine Models on the Attack of Malicious Objects in Computer Network

1Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835215, India
2Department of Applied Mathematics, Nilai Educational Trust's Group of Institutions, Thakurgaon, Ranchi 835205, India

Received 5 April 2011; Accepted 3 June 2011

Academic Editor: Zidong Wang

Copyright © 2012 Bimal Kumar Mishra and Aditya Kumar Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

SEIQR (Susceptible, Exposed, Infectious, Quarantined, and Recovered) models for the transmission of malicious objects with simple mass action incidence and standard incidence rate in computer network are formulated. Threshold, equilibrium, and their stability are discussed for the simple mass action incidence and standard incidence rate. Global stability and asymptotic stability of endemic equilibrium for simple mass action incidence have been shown. With the help of Poincare Bendixson Property, asymptotic stability of endemic equilibrium for standard incidence rate has been shown. Numerical methods have been used to solve and simulate the system of differential equations. The effect of quarantine on recovered nodes is analyzed. We have also analyzed the behavior of the susceptible, exposed, infected, quarantine, and recovered nodes in the computer network.