An Epidemic Model of Computer Worms with Time Delay and Variable Infection Rate

Abstract

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.

Group-Based Susceptible-Infectious-Susceptible Model in Large-Scale Directed Networks

“…When further declines, i.e., = 0.0011 and 0.001, the analytical results are able to match the simulation results from the beginning to the end. According to (20), the epidemic threshold is given by * = 0.001. This figure reveals that the proposed mean-field model is asymptotically accurate with a decreasing and is able to precisely describe the epidemic propagation when the effective spreading rate is around the epidemic threshold.…”

“…The infection density at = 1000 is used as the stable infection density, as indicated by the -axis. Evaluated with (20), the epidemic threshold is * = 0.005, 0.0033, and 0.0025 when = 4, 6, and 8, respectively. We can see from…”

“…The probability of a node switching to the "warning" state depends on the population of nodes in the warning state and is independent of the network topology. The SIS model was extended with "quarantined", "vaccinated", and "delay" states, to capture the time-delayed worm propagation in computer networks [20]. These models significantly simplified the dynamic process by omitting the impact of network topologies.…”

Numerical Treatment for Stochastic Computer Virus Model

“…A time-delayed SIQVD worm propagation model with variable infection rate was framed. This model can be utilized for internet worms [Yao, Fu, Yang et al (2018)]. A research has been conducted on the susceptible, latent, breaking-out, quarantine and susceptible (SLBQRS) computer virus model.…”

A Stochastic Numerical Analysis for Computer Virus Model with Vertical Transmission over the Internet

“…A time-delayed SIQVD worm propagation model with variable infection rate was framed. This model can be utilized for internet worms [Yao, Fu, Yang et al (2018)]. Research has been conducted on the susceptible, latent, breaking-out, quarantine and susceptible (SLBQRS) computer virus model.…”