Modeling And Stability Analysis Of Internet Worm With Two Delays

With the rapid development of Internet technology, network has entered every corner of people’s daily life. As it brings convenience to people’s lives, it also creates conditions for worms to spread. Establish worm propagation model is one of the important means for us to study worm propagation. However, the real propagation of worms is very complex, for the remove of worms, the reinstallation of system and the lurking behavior of worms will bring a variety of time delays for worm propagation. The traditional single delay worm propagation model doesn’t work well for the worm propagation in real word, therefore nowadays how to accurately predict worm propagation in real word has become an important issue.Based on the achievement of epidemiology and nonlinear dynamics, this thesis analyzes and models the influence on worm propagation results from the time delay caused by removing worms and establishs an SIDV worm propagation model with time delay. Then the thesis analyzes its stability and conduct numerical experiments.In order to predict worm propagation more realistically and constrain the propagation of worms, based on the SIDV model, a quarantine strategy is proposed based on a intrusion detection system. Among the intrusion detection system, misuse detection system improves the rate of detection by setting the time window. Time window may lead to time delay. Therefore, the thesis constructs a worm propagation model with two time delays and analyzes its stability and Hopf bifurcation. Through theoretical analysis, each of the two delays has its corresponding critical value. When the two delays are both less than their critical value, the worm propagation system is stable and easy to control. In addition, the number of infected hosts decreases significantly. Whereas when either of the two delays or both of them exceeds their corresponding critical value, Hopf bifurcation appears so that the system is out of control and the containment strategy does not work. Therefore, people should remove the worm immediately after the hosts are infected, and the value of time window in intrusion detection system must less than its critical value, so as to ensure the stability of the worm propagation system. In order to verify the correctness of theoretical analysis, the thesis makes numerical experiments and simulation experiments and the results shows its correctness.