A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism
Abstract
:1. Introduction
2. Numerous Concepts Associated with the Field of Fractional Calculus
- 1.
- and exhibit continuity throughout .
- 2.
- for all , with and consisting of a pair of positive variables.
3. Description of the Model
- (i)
- When an Ignorant has contact with a Latent, the Ignorant is affected and becomes a Latent with the possibility of , where denotes the rumor contact rate, denotes the saturation constant, and implies the level of the media reports. Obviously, as . The timely popularization of scientific knowledge and countering rumors through media reports can help control rumors to a certain extent. The influence of media reports on communication is not inherently decisive, Ref. [15]. The transmission rate is influenced by media reports in Figure 1.
- (ii)
- Some Latents may tend to become Spreaders with a transfer rate and the parameter represents the recovery rate of Spreaders when they are exposed to the impacts of the forgetting mechanism.
- (iii)
- represents a saturated treatment function that represents the nonlinear inhibition mechanism, where and . means the highest level of inhibition measure for the Spreaders group.
- (iv)
- We make the assumption that the rate of immigration is , while the rate of emigration is . All the parameters of the model are assumed to possess constant and positive values.
4. Analysis of the Model
5. Fractional Optimal Control of the Model
6. ILSR Rumor Model with Fractional Stochastic
7. Sensitivity Analysis and Numerical Simulation
7.1. Sensitivity Analysis
7.2. Numerical Simulation
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Yue, X.; Zhu, W. A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism. Symmetry 2024, 16, 602. https://doi.org/10.3390/sym16050602
Yue X, Zhu W. A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism. Symmetry. 2024; 16(5):602. https://doi.org/10.3390/sym16050602
Chicago/Turabian StyleYue, Xuefeng, and Weiwei Zhu. 2024. "A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism" Symmetry 16, no. 5: 602. https://doi.org/10.3390/sym16050602
APA StyleYue, X., & Zhu, W. (2024). A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism. Symmetry, 16(5), 602. https://doi.org/10.3390/sym16050602