Dynamic model of worm propagation in computer network

Abstract

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 Rv<1, and unstable if Rv>1. 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.