With rapid development of Internet, network security issues become increasingly serious. Temporary patches have been put on the infectious hosts, which may lose efficacy on occasions. This leads to a time delay when vaccinated hosts change to susceptible hosts. On the other hand, the worm infection is usually a nonlinear process. Considering the actual situation, a variable infection rate is introduced to describe the spread process of worms. According to above aspects, we propose a time-delayed worm propagation model with variable infection rate. Then the existence condition and the stability of the positive equilibrium are derived. Due to the existence of time delay, the worm propagation system may be unstable and out of control. Moreover, the threshold 0 of Hopf bifurcation is obtained. The worm propagation system is stable if time delay is less than 0 . When time delay is over 0 , the system will be unstable. In addition, numerical experiments have been performed, which can match the conclusions we deduce. The numerical experiments also show that there exists a threshold in the parameter , which implies that we should choose appropriate infection rate ( ) to constrain worm prevalence. Finally, simulation experiments are carried out to prove the validity of our conclusions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.