Dynamic model of worm propagation in computer network

In this paper, an attempt has been made to mathematically formulate a compartmental susceptible – exposed – infectious – susceptible with vaccination (that is, anti-virus treatment) (SEIS-V) epidemic transmission model of worms in a computer network with natural death rate (which depends on the tota...

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Bibliographic Details
Published in:Applied mathematical modelling 2014-04, Vol.38 (7-8), p.2173-2179
Main Authors: Mishra, Bimal Kumar, Pandey, Samir Kumar
Format: Article
Language:English
Subjects:
Asymptotic properties
Compartmental model
Computer networks
Computer programs
Computer worms
Dynamic models
Equilibrium
Mathematical analysis
Mathematical models
Modified reproductive number
Stability
Vertical transmission
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Summary:In this paper, an attempt has been made to mathematically formulate a compartmental susceptible – exposed – infectious – susceptible with vaccination (that is, anti-virus treatment) (SEIS-V) epidemic transmission model of worms in a computer network with natural death rate (which depends on the total number of nodes). The stability of the result is stated in terms of modified reproductive number Rv. We have derived an explicit formula for the modified reproductive number Rv, and have shown that the worm-free equilibrium, whose component of infective is zero, is globally asymptotically stable if Rv1. The contribution of vertical transmission to the modified reproductive number is also analyzed. Numerical methods are employed to solve and simulate the system of equations developed and interpretation of the model yields interesting revelations. Analysis of efficient antivirus software is also performed.
ISSN:0307-904X
DOI:10.1016/j.apm.2013.10.046