SEIQRS model for the transmission of malicious objects in computer network

被引：155

作者：

Mishra, Bimal Kumar ^{[1
]}

Jha, Navnit ^{[2
]}

机构：

[1] Birla Inst Technol, Dept Appl Math, Ranchi 835215, Bihar, India

[2] Rajiv Gandhi Inst Petr Technol, Dept Math, Rae Bareli 229316, India

来源：

APPLIED MATHEMATICAL MODELLING | 2010年 / 34卷 / 03期

关键词：

Epidemic model; Quarantine; Endemic equilibrium; Asymptotic stability; Malicious objects; Computer network; ARBITRARILY DISTRIBUTED PERIODS; SEIRS EPIDEMIC MODEL; MATHEMATICAL-THEORY; ENDEMIC MODELS; GLOBAL STABILITY; DYNAMICS; BIFURCATION; QUARANTINE;

D O I：

10.1016/j.apm.2009.06.011

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Susceptible (S) - exposed (E) - infectious (1) - quarantined (Q) - recovered (R) model for the transmission of malicious objects in computer network is formulated. Thresholds, equilibria, and their stability are also found with cyber mass action incidence. Threshold R-cq determines the outcome of the disease. If R-cq <= 1, the infected fraction of the nodes disappear so the disease die out, while if R-cq > 1, the infected fraction persists and the feasible region is an asymptotic stability region for the endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. 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. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：710 / 715

页数：6

共 46 条

[11]

Forrest S., 1994, Proceedings of 1994 IEEE Computer Society Symposium on Research in Security and Privacy (Cat. No.94CH3444-7), P202, DOI 10.1109/RISP.1994.296580

[12] Dealing with software viruses: A biological paradigm [J].

Electrical and Electronic Engineering Department, Imperial College, London, SW7 2BT, United Kingdom .

Information Security Technical Report, 2007, 12 (04) :242-250

[13]

Gelenbe E, 2004, LECT NOTES COMPUT SC, V3280, P667

[14]

Gelenbe Erol, 2005, LECT NOTES COMPUTER, V3733

[15] Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity [J].

Greenhalgh, D .

MATHEMATICAL AND COMPUTER MODELLING, 1997, 25 (02) :85-107

[16] Effects of quarantine in six endemic models for infectious diseases [J].

Hethcote, H ;

Ma, Z ;

Liao, SB .

MATHEMATICAL BIOSCIENCES, 2002, 180 :141-160

[17]

Hethcote H.W., 1981, Differential Equations and Applications in Ecology, Epidemics and Population Problems, Claremont Conference Proceedings, P65

[18] SOME EPIDEMIOLOGIC MODELS WITH NONLINEAR INCIDENCE [J].

HETHCOTE, HW ;

VANDENDRIESSCHE, P .

JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 29 (03) :271-287

[19] Networks and epidemic models [J].

Keeling, MJ ;

Eames, KTD .

JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2005, 2 (04) :295-307

[20]

Kephart J.O., 1995, P INT JOINT C ART IN

← 1 2 3 4 5 →