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

Zhang, Zizhen; Upadhyay, Ranjit Kumar; Bi, Dianjie; Wei, Ruibin

doi:10.1155/2018/8239823

Cited by 3 publications

(2 citation statements)

References 31 publications

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“…More SLB models were observed in the following studies; [24,25]. Other models which have been used to represent virus propagation in computers alongside detachable storage, external computers, and age structure using the susceptible-infected-countermeasure (SIC) model [7], strongly protected susceptible-weakly protected susceptible-infective-external (SWIE) model [6] and susceptible-infected-recovered (SIR) model [2].…”

Section: Related Literaturementioning

confidence: 99%

An Epidemic Patch-Enabled Delayed Model for Virus Propagation: Towards Evaluating Bifurcation and White Noise

Liu

Madhusudanan²,

Srinivas

et al. 2022

Mathematical Problems in Engineering

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The massive disruptions caused by malware, such as a virus in computer networks and other aspects of information and communication technology, have generated attention, making it a hot research topic. While antivirus and firewalls can be effective, there is also a need to understand the spread patterns of viral infection using epidemic models to curb its incidences. Many previous research attempts have produced analytical models for computer viruses under various infectiousness situations. As a result, we suggested the SLBS model, which considers infection latency and transient immunity in patched nodes. Under certain conditions, the local stability of all equilibrium points is investigated. By setting the delay parameter, we established the occurrence of a Hopf bifurcation (HB) as it crossed a crucial point by several analyses. We also used the centre manifold theorem and normal form theory to examine the attributes of the HB. While the former was used to study the time delay and direction of Hopf bifurcation, the latter was used to investigate external noise and its intensities. Finally, numerical simulations two dimensional and three-dimensional graphs were used to depict the perturbations of the model, thus bolstering the essentiality of the study.

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Section: Related Literaturementioning

confidence: 99%

An Epidemic Patch-Enabled Delayed Model for Virus Propagation: Towards Evaluating Bifurcation and White Noise

Liu

Madhusudanan²,

Srinivas

et al. 2022

Mathematical Problems in Engineering

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“…A general formal study to obtain the reproduction number and discuss the positivity and stability properties of equilibrium points is proposed and formally discussed [34]. Existence and stability of equilibrium points of the models have been extensively studied [35], [36]. Consequently, epidemic models about malwares is used for reference in our study.…”

Section: B Literature Reviewmentioning

confidence: 99%

Interplay Between Malware Epidemics and Honeynet Potency in Industrial Control System Network

Yao

Sheng

et al. 2020

IEEE Access

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The Industrial Control System (ICS) is widely used in industrial processes, such as power grids, water conservancy, natural gas, petrochemical and so on. More and more cyber attacks are targeting the ICS worldwide. This paper presents a novel honeynet-based epidemic model in ICS network. The honeynet is an active approach that can attract malware attacks and provide sample information and immunization strategy of the malware. An epidemic model with immunization and quarantine in ICS network is formulated to explore the dynamics of the malware propagation, and the honeynet potency is analyzed as well. Theoretical analysis reveals the disease-free and endemic equilibrium of our model, then the local and global stability of the disease-free (endemic) equilibrium are examined by the basic reproduction number. Furthermore, numerical experiments show that the honeypot with more system vulnerabilities is conducive to suppress the malware epidemic, and the honeynet with lower average degree power low index can be more effectively. In addition, simulation experiments provide the actual behavior of malware propagation in the ICS network and verification of our derivations.

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HOPF- bifurcation analysis of delayed computer virus model with holling type iii incidence function and treatment

Madhusudanan¹,

Srinivas

Nwokoye

et al. 2022

Scientific African

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

Cited by 3 publications

References 31 publications

An Epidemic Patch-Enabled Delayed Model for Virus Propagation: Towards Evaluating Bifurcation and White Noise

An Epidemic Patch-Enabled Delayed Model for Virus Propagation: Towards Evaluating Bifurcation and White Noise

Interplay Between Malware Epidemics and Honeynet Potency in Industrial Control System Network

HOPF- bifurcation analysis of delayed computer virus model with holling type iii incidence function and treatment

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