Epidemic model on rumor propagation in e-commerce

Kishore, Rajeev; Tyagi, Indu; Rao, Yerra Shankar; Kumar, Deepak

doi:10.1016/j.matpr.2021.11.263

Cited by 1 publication

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 4 (GAS of the rumor-spreading equilibrium point). The rumor-spreading equilibrium point  * is not only locally asymptotically stable but also globally asymptotically stable with respect to the set W* given in (7) provided that it exists.…”

Section: Stability Of the Model With Smooth Control Functionsmentioning

confidence: 99%

“…It is well-known that controlling rumors is an important social issue, especially in the context of the rapidly evolving Internet and social media sites and platforms For this reason, many mathematicians and engineers have studied a broad range of mathematical models based on basic principles of compartment epidemiological models for describing the transmission of rumors (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12]). These models have various useful applications in real-world situations and can suggest effective and suitable strategies to control the spreading of rumors.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lyapunov functions for studying global asymptotic stability of two rumor spreading models

Hoang

2023

Commun. Theor. Phys.

View full text Add to dashboard Cite

In a previous work (2018, Commun. Theor. Phys. 70, 795–802), a new compartment model for the spreading of rumors was introduced and analyzed. However, only the local asymptotic stability of this model was discussed. In the present work, we first provide a rigorous mathematical analysis for the global asymptotic stability (GAS) of the above-mentioned rumor spreading model. By constructing suitable Lyapunov candidate functions, we obtain the GAS of a rumor-free (boundary) equilibrium point and a unique rumor-spreading (positive) equilibrium point. After that, we utilize the approach based on the Lyapunov candidate functions to study the GAS of another rumor spreading model with control strategies, which was proposed in (2022, Physica A 606, 128157). As an important consequence, the GAS of the rumor spreading model with control strategies is determined fully without resorting to technical hypotheses used in the benchmark work. Lastly, the theoretical findings are supported by a set of illustrative numerical examples. The obtained results not only improve the ones constructed in the two above-mentioned benchmark papers but also can be extended to study the global dynamics of other rumor propagation models in the context of both integer-order and fractional-order derivatives.

show abstract

Section: Stability Of the Model With Smooth Control Functionsmentioning

confidence: 99%