Global exponential stability of nonresident computer virus models

Tang, Canqin; Wu, Yonghong

doi:10.1016/j.nonrwa.2016.08.003

Cited by 11 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Table lists five sets of parameters designed based on statistics and data from . The CTMC in Figure is analyzed using these parameter sets to study effects of different model parameters on the attack success probability.…”

Section: Continuous‐time Markov Chain–based Time‐dependent Solution Amentioning

confidence: 99%

Probabilistic modeling and analysis of sequential cyber‐attacks

Liu

Xing

Zhou

2019

Engineering Reports

View full text Add to dashboard Cite

Security is one of the major challenges for promoting the computer industry. Existing models for assessing security have mostly assumed that different hazards causing the security breach are independent of each other. Dependencies however can exist among different hazardous actions and they may affect the system security attribute greatly. This paper advances the state of the art in quantitative security risk assessment by modeling one such dependency, where multiple sequence‐dependent hazardous actions are performed to launch a successful security cyber‐attack. Continuous‐time Markov chain and semi‐Markov process–based methods are proposed to estimate the occurrence probability of a security risk for systems undergoing the sequential cyber‐attacks. While the CTMC method is limited to the exponential state transition time, the proposed semi‐Markov process–based approach is applicable to analyzing attacks with any arbitrary types of transition time distributions. Both methods are illustrated using case studies where Trojan attacks in the banking application are modeled and analyzed.

show abstract

Section: Continuous‐time Markov Chain–based Time‐dependent Solution Amentioning

confidence: 99%

Probabilistic modeling and analysis of sequential cyber‐attacks

Liu

Xing

Zhou

2019

Engineering Reports

View full text Add to dashboard Cite

show abstract

“…In the past decades, some mathematical models describing malicious codes propagation are proposed to study viruses' behavior. For example, the classic epidemic models [5][6][7][8][9], the models with graded infection rate [10][11][12][13][14][15][16][17][18], the stochastic models [19][20][21][22][23] and some other models [2,[24][25][26].…”

Section: Introductionmentioning

confidence: 99%

A Delayed Epidemic Model for Propagation of Malicious Codes in Wireless Sensor Network

2019

View full text Add to dashboard Cite

In this paper, we investigate a delayed SEIQRS-V epidemic model for propagation of malicious codes in a wireless sensor network. The communication radius and distributed density of nodes is considered in the proposed model. With this model, first we find a feasible region which is invariant and where the solutions of our model are positive. To show that the system is locally asymptotically stable, a Lyapunov function is constructed. After that, sufficient conditions for local stability and existence of Hopf bifurcation are derived by analyzing the distribution of the roots of the corresponding characteristic equation. Finally, numerical simulations are presented to verify the obtained theoretical results and to analyze the effects of some parameters on the dynamical behavior of the proposed model in the paper.

show abstract

“…However, as stated in [20], those above models with the exposed compartment neglect the fact that a computer can infect other computers through file copying or file downloading. Therefore, to overcome the above-mentioned defect, computer virus models with infectivity in latent period have received much attention in recent years [21][22][23][24][25][26]. Unfortunately, most of these models still have some defects.…”

Section: Introductionmentioning

confidence: 99%

Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software

Zhang

Upadhyay

et al. 2018

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system.

show abstract

Global exponential stability of nonresident computer virus models

Cited by 11 publications

References 18 publications

Probabilistic modeling and analysis of sequential cyber‐attacks

Probabilistic modeling and analysis of sequential cyber‐attacks

A Delayed Epidemic Model for Propagation of Malicious Codes in Wireless Sensor Network

Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software

Contact Info

Product

Resources

About