Dynamical Behavior Analysis of a Time-Delay SIRS-L Model in Rechargeable Wireless Sensor Networks

Liu, Guiyun; Li, Junqiang; Liang, Zhongwei; Peng, Zhimin

doi:10.3390/math9162007

Cited by 9 publications

(1 citation statement)

References 30 publications

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“…All malware mathematical models are based on a mix of these common states, developing specific transitions between them according to the modeled network. Examples can be found in SIRS models [22,23], SEIRS models [24][25][26], or SEIRD models [27,28]), to cite the most popular combinations. On top of them, innumerable variations introduce one or more new subdynamics, e.g., [22], where an SIRS-L model was proposed to account for the low-energy mode of wireless sensors.…”

Section: Review Of Literature Modelsmentioning

confidence: 99%

Deriving Exact Mathematical Models of Malware Based on Random Propagation

Carnier,

Li,

Fujimoto

et al. 2024

Mathematics

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The advent of the Internet of Things brought a new age of interconnected device functionality, ranging from personal devices and smart houses to industrial control systems. However, increased security risks have emerged in its wake, in particular self-replicating malware that exploits weak device security. Studies modeling malware epidemics aim to predict malware behavior in essential ways, usually assuming a number of simplifications, but they invariably simplify the single most important subdynamics of malware: random propagation. In our previous work, we derived and presented the first exact mathematical model of random propagation, defined as the subdynamics of propagation of a malware model. The propagation dynamics were derived for the SIS model in discrete form. In this work, we generalize the methodology of derivation and extend it to any Markov chain model of malware based on random propagation. We also propose a second method of derivation based on modifying the simplest form of the model and adjusting it for more complex models. We validated the two methodologies on three malware models, using simulations to confirm the exactness of the propagation dynamics. Stochastic errors of less than 0.2% were found in all simulations. In comparison, the standard nonlinear model of propagation (present in ∼95% of studies) has an average error of 5% and a maximum of 9.88% against simulations. Moreover, our model has a low mathematical trade-off of only two additional operations, being a proper substitute to the standard literature model whenever the dynamical equations are solved numerically.

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Section: Review Of Literature Modelsmentioning

confidence: 99%

Deriving Exact Mathematical Models of Malware Based on Random Propagation

Carnier,

Li,

Fujimoto

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

Epidemic Models of Malicious-Code Propagation and Control in Wireless Sensor Networks: An Indepth Review

Nwokoye¹,

Madhusudanan²

2022

Wireless Pers Commun

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Effect of Delay in SMS Worm Propagation in Mobile Network with Saturated Incidence Rate

Zhang

Madhusudanan²,

Murthy

2023

Wireless Pers Commun

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Cell phones are getting increasingly well known. SMS worms spread themselves by sending messages, which can rapidly taint a large number of cell phones and cause incredible harm to clients. Consequently, it is critical to investigate and foresee the proliferation of SMS worms to diminish their expected danger. In this article, we propose a worm spread model in light of SMS, named SAID (Susceptible-Affected-Infected-suspended) with a saturated incidence rate and time delay. To precisely foresee the worm proliferation by means of SMS, first, we add the impacted state to address the condition of clients who have gotten the messages yet have not tapped the malignant connections. Second, since an infected node doesn't necessarily send pernicious messages to other people, a novel express, the suspended state, which gets some margin to affected node to infected node in mobile network. Specifically, nonlinear stability, hopf bifurcation and its direction and steadiness of the periodic solution not entirely settled by utilizing the centre manifold theorem. At last, a few numerical simulations are presented to check the analytical results.

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Dynamical Behavior Analysis of a Time-Delay SIRS-L Model in Rechargeable Wireless Sensor Networks

Cited by 9 publications

References 30 publications

Deriving Exact Mathematical Models of Malware Based on Random Propagation

Deriving Exact Mathematical Models of Malware Based on Random Propagation

Epidemic Models of Malicious-Code Propagation and Control in Wireless Sensor Networks: An Indepth Review

Effect of Delay in SMS Worm Propagation in Mobile Network with Saturated Incidence Rate

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