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Rumor and counter-rumor dynamics in a stochastic delay-fractional framework: a GL-NSFD approach
Ali Raza1,2, Marek Lampart3, Umar Shafique3,4
1IT4Innovations, VSB-Technical University of Ostrava, 17 listopadu 2172/15, Ostrava, 708 33, Czech Republic. ali.raza@vsb.cz.
Scientific Reports
|May 13, 2026
Summary
This study models rumor propagation using a stochastic fractional delay differential equation. The research analyzes stability and uses numerical methods to validate the model for understanding social media information dynamics.
Area of Science:
- Mathematical modeling of social phenomena
- Epidemiology
- Computational mathematics
Background:
- Social media facilitates rapid rumor spreading, posing societal challenges.
- Understanding rumor dynamics is crucial for information management.
- Existing models may not fully capture the complexities of rumor propagation.
Purpose of the Study:
- To develop a novel stochastic fractional delay differential equation (SFDDE) model for rumor propagation.
- To analyze the stability of equilibrium points in the rumor dynamics model.
- To investigate the role of the reproduction number in rumor dissemination.
Main Methods:
- Formulation of a four-compartment SFDDE model (susceptible, spreaders, counter-rumor spreaders, stiflers).
- Analytical investigation of model properties: nonnegativity, boundedness, local and global stability.
- Application of the Generalized Nonstandard Finite Difference (GL-NSFD) method for numerical simulations.
Main Results:
- Established nonnegativity and boundedness of model solutions.
- Determined the local and global stability of Rumor-Free and Rumor-Present Equilibria.
- Identified the reproduction number as a critical threshold parameter for rumor spread.
- Validated model accuracy and efficiency through numerical simulations and graphical analysis.
Conclusions:
- The SFDDE model provides a robust framework for studying rumor propagation.
- Stability analysis and numerical methods confirm the model's predictive capabilities.
- The study offers insights into controlling and mitigating the spread of misinformation online.
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