A delayed e-epidemic SLBS model for computer virus

Zhang, Zizhen; Kumari, Sangeeta; Upadhyay, Ranjit Kumar

doi:10.1186/s13662-019-2341-8

Cited by 12 publications

(5 citation statements)

References 46 publications

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“…Similarly, Zhao and Bi [21] used the SLBQR to model virus spread with two-time delays and the existence of Hopf bifurcation. Another delayed version of the SLBS model was developed by Zhang et al [22] and after studying its stability analyses. Because most models only represent horizontal transmission (HT), Zhu et al [23] utilized the SLBR model to represent both HT and vertical transmission of viruses in a computer network.…”

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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“…Numerous scholars have examined time-delay differential equation (DDE) and in recent decades (see, for example, [27][28][29][30]), since they are extremely useful for modelling a broad number of scenarios in traditional fields like engineering and science, as well as relatively new fields like transmission of infection, clinical science, optimized drug rehabilitation, bio-economics, farming, financial management, insurance, and protection of the environment. Many fields, including population trends [31], epidemiology [32], and computer systems [33,34], have adopted DDE for investigation.…”

Section: Introductionmentioning

confidence: 99%

The design of novel intelligent paradigms for future prediction smoking model with saturated occurrence rate

Nisar

Shoaib

Zubair

et al. 2022

Preprint

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The approach of artificial neural network backpropagation with Levenberg Marquardt algorithm (LMA) and Bayesian Regularization algorithm (BRA) is used to analyze the smoking model in this study. We start by looking at a delayed smoking model wherein potential smokers be supposed to meet the logistic equation. As in manner of Delayed Differential Equations (DDEs), we analyze the dynamic characteristics of the developed framework and provide criteria regarding asymptotic stability of the system in steady condition. The model's Hopf bifurcation study is also addressed. The Adam numerical approach is used to build the reference dataset in Mathematica. The numerical and graphical results to the smoking problem is then interpreted using this dataset in MATLAB. The validity of applied techniques is validated using regression plots, MSE curves, and error histogram.

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“…Using the method of characteristics [3], [4], [5], [6], [8], [9], [11], [24], [53], [55], [58] and method of steps from the theory of delayed differential equations [12], [28], [46], [57], [59], we obtain an exact solution of the SIPCV epidemic model. This solution is given in form of the recurrent formulae (like in works [3], [4], [8], [55]) in which the densities of all subpopulations are defined through the integrals from solution taken at previous instance of time.…”

Section: Introductionmentioning

confidence: 99%

Age-structured delayed SIPCV epidemic model of HPV and cervical cancer cells dynamics I. Numerical method

Akimenko¹,

Adi-Kusumo²

2021

BIOMATH

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The numerical method for simulation dynamics of nonlinear epidemic model of age-structured sub-populations of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) is developed (SIPCV model). Cell population dynamics is described by the initial-boundary value problem for the delayed semi-linear hyperbolic equations with age- and time-dependent coefficients and HPV dynamics is described by the initial problem for nonlinear delayed ODE. The model considers two time-delay parameters: the time between viral entry into a target susceptible cell and the production of new virus particles, and duration of the first stage of delayed immune response to HPV population growing. Using the method of characteristics and method of steps we obtain the exact solution of the SIPCV epidemic model in the form of explicit recurrent formulae. The numerical method designed for this solution and used the trapezoidal rule for integrals in recurrent formulae has a second order of accuracy. Numerical experiments with vanished mesh spacing illustrate the second order of accuracy of numerical solution with respect to the benchmark solution and show the dynamical regimes of cell-HPV population with the different phase portraits.

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A delayed e-epidemic SLBS model for computer virus

Cited by 12 publications

References 46 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

The design of novel intelligent paradigms for future prediction smoking model with saturated occurrence rate

Age-structured delayed SIPCV epidemic model of HPV and cervical cancer cells dynamics I. Numerical method

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