Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy

Sabbar, Yassine; Din, Anwarud; Kiouach, Driss

doi:10.1016/j.chaos.2023.113434

Cited by 14 publications

(28 citation statements)

References 30 publications

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“…One can investigates some other classical questions such as the extinction, the permanence, the persistence in the mean, and the existence of a unique stationary distribution for the infected nodes variable I(t). We note that these concernes are often discussed in the literature and use the SDE background theory (see for instance [11,13,27,[35][36][37]). The investigation of these questions for SDE (3.5) represents a real challenge in our futur papers.…”

Section: 10)mentioning

confidence: 99%

Stochastic modeling of malware propagation on reduced scale-free topology-based wireless sensor networks: dynamics, resilience, and countermeasures

B'ayir,

Essouifi,

El Ansari

et al. 2024

J. Math. Computer Sci.

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In this paper, we present an approach to model the stochastic spread of malware within a wireless sensor network (WSN). The network is characterized as a reduced scale-free topology, exhibiting just two average degrees. Our work delves into the realm of stochastic epidemic modeling building upon its deterministic counterpart [19]. We leverage two distinct methodologies, namely the discrete-time Markov chain (DTMC) and the Stochastic Differential Equation (SDE) techniques, to explore the temporal dynamics of our proposed model. Our investigation extends to analyzing how various model parameters influence infection within WSNs. Through Monte Carlo simulations and the Euler-Maruyama discretization scheme, we validate the credibility of our two stochastic models by demonstrating their congruences and their fluctuations around the deterministic solution reliant on nonlinear coupled ordinary differential equations (ODEs). This comparison is guided for the best understanding of the stochastic fluctuations effect in the dynamics of the spread of malware in WSNs. Our findings offer valuable insights, indicating that the network exhibits enhanced resilience against network failures and more balanced energy consumption when specific countermeasures are implemented. This probabilistic framework proves both meticulous and systematic, providing a profound understanding of the intricate randomness inherent in the behavioral patterns of malware within WSNs.

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Section: 10)mentioning

confidence: 99%

Stochastic modeling of malware propagation on reduced scale-free topology-based wireless sensor networks: dynamics, resilience, and countermeasures

B'ayir,

Essouifi,

El Ansari

et al. 2024

J. Math. Computer Sci.

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“…Under (A), system (2) is mathematically well-defined and has a unique postive solution [24]. In other words, it is a model that provides a reliable and accurate representation of the biological disease being studied.…”

Section: Hypothetical Frameworkmentioning

confidence: 99%

Asymptotic extinction and persistence of a perturbed epidemic model with different intervention measures and standard Lévy jumps

Sabbar

2023

BBM

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Controlling an outbreak through response measures is critical to saving lives and protecting vulnerable populations. This article proposes an epidemic model with three intervention measures: media coverage, isolation, and medical therapy. Since randomness plays an important role in biology, from the molecular level to the organismal level, we extend our system to a more realistic framework, which then takes into account the effect of standard jumps due to some sudden environmental changes. After providing the associated framework, the sharp criteria for asymptotic extinction and persistence of illness are derived. To check the accuracy of our results, we perform two numerical examples.

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“…As highlighted in references [11][12][13][14][15][16][17][18], the use of mathematical modeling tools is highly advised for examining the dynamics of epidemic spread and developing successful control strategies. These models provide a well-rounded approach by bridging the gap between biological scenario to show the infection's natural progression and its dependency on the associated data.…”

Section: Introductionmentioning

confidence: 99%

Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise

Ain,

Din,

Qiang

et al. 2024

Fractal Fract

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In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.

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Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy

Cited by 14 publications

References 30 publications

Stochastic modeling of malware propagation on reduced scale-free topology-based wireless sensor networks: dynamics, resilience, and countermeasures

Stochastic modeling of malware propagation on reduced scale-free topology-based wireless sensor networks: dynamics, resilience, and countermeasures

Asymptotic extinction and persistence of a perturbed epidemic model with different intervention measures and standard Lévy jumps

Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise

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