Local asymptotic stability of a modified mathematical defense model for complex computer networks

Abstract

This study focuses on the potential threat for virus spread in complex computer networks using epidemic theory. We propose a modified Susceptible-Exposed-Infectious-Susceptible (SEI-S)model, to characterize the dynamics of the virus spread in the computer network. This is a modification to the traditional SEI model. Threshold, equilibrium and local asymptotic stability are derived and discussed. The system is stable (the virus dies out) if the derived threshold value (reproduction number) is less than or equal to 1 and is unstable (the virus persists and spreads) if the threshold is greater than 1.The Runge–Kutta–Fehlberg order 4 and 5 numerical method is employed using MATLAB to solve the system ofordinary differential equations and to simulate the system. The issues and concerns about security in the cyber-world make it overly necessary to invest research efforts so as to provide countermeasures for virus propagation.

Keywords: Local asymptotic stability, Epidemic model, Computer network,Virus