Analysis Of A Delayed Internet Worm Propagation Model Based On Pulse Quarantine Strategy

With the rapid development of computer technology, operating systems and softwares become more and more complex, and their vulnerabilities leave an opportunity for worms to spread. Among them, the spread of worms that exploit0-day vulnerabilities bring great damage to the network and cause huge loss to the users. Due to the lack of effective defensive strategy such as safety patch, the measures users utilize to deal with worms could hardly work well. Thus, it leaves risks that the worm may break out again.In this paper, on the basis of epidemiology and nonlinear dynamics, we model the complex phenomenon of worm propagation, which results from the time delay caused by removing worms. We establish an SIDV worm propagation model with time delay, analyze its stability and conduct numerical experiments. After that, we put forward two containment strategies to control the spread of worms. We discuss their effectiveness by theoretical analysis, numerical experiments and simulation experiments.Initially, we introduce basic principles of vulnerability exploitation and network worm. After researching some classical worm propagation models, we establish an SIDV worm propagation model with time delay caused by vaccination and analyze its stability and Hopf bifurcation. Theoretical analysis and numerical experiments show that there is a threshold To in SIDV model. When time delay is less than the threshold τ0, the system is stable and easy to control; when time delay is larger than the threshold, a Hopf bifurcation appears. We then put forward constant quarantine strategy to control the spread of worm and establish the SIDQV worm propagation model with constant quarantine strategy. Through theoretical analysis and numerical experiments, we find that it does not eliminate bifurcation phenomenon but has some containment impact on the spread of worms. At last, we propose pulse quarantine strategy and establish SIDQV worm propagation model with pulse quarantine strategy. We prove its effectiveness on the spread of worm propagation, which means that SIDQV worm propagation model with pulse quarantine strategy could make system stable, the trends of worm propagation could be predicted and worms could be eliminated. We verify the correctness of thereotical analysis and numerical experiments by simulation experiments.