MATHEMATICAL MODELING OF MISINFORMATION SPREAD USING FRACTIONAL DIFFERENTIAL EQUATIONS

Naila Afzal; Fazal Haq; Muhammad Azeem Ullah Siddique

doi:10.71146/kjmr924

Authors

Naila Afzal Department of Mathematics, Government College University Lahore (GCUL), Pakistan. Author
Fazal Haq Department of Mathematics, The University of Agriculture Swat (UoAS), Pakistan. Author
Muhammad Azeem Ullah Siddique PhD Scholar, Department of Mathematical Science Research Center, Federal Urdu University Arts Science and Technology, Pakistan. Author

DOI:

https://doi.org/10.71146/kjmr924

Keywords:

Misinformation spread, fractional differential equations, memory effects, media influence, SIR model, numerical simulation

Abstract

Background: The dissemination of false information over the social media and the digital space has become a pressing concern. Conventional epidemic models do not respond to complex interactions of misinformation transmission, in particular the impact of memory and response latency. Fractional differential equations (FDEs) provide the potential solution since they consider these memory effects and it can be used to provide a more accurate description of misinformation dynamics.

Purpose: The aim of the current research is to create a fractional-order model that will examine the diffusion of misinformation, with memory effects and non-local interactions.

Method: The model is a variant of the Susceptible-Infected-Recovered (SIR) model, in which the rate of change is characterized by the application of a set of fractional derivatives. The equations of fractional-order are solved numerically by use of the Grunwald-Letnikov approximation. The model analyzes how the rate of transmission, recovery and media influence spread misinformation.

Result: The experiment concludes that the fractional order reduces the speed of the spread and the level of infection, which means that memory effects play a big role in the processes of misinformation. An increase in the rate of transmission and media impact increases the rate of spread, and the recovery rates reduce the time of misinformation.

Conclusion: Fractional-order model gives a realistic description of the misinformation dynamics as compared to the traditional models because it takes into account memory influences. The findings highlight the need to contain the transmission rates, media influence, and timely corrective actions in order to reduce the misinformation.

Downloads

Download data is not yet available.

References

Caputo, M. (2025). Fractional calculus and its application to the spreading of misinformation. Journal of Mathematical Modeling, 22(4), 459–474.

Chen, Y., & Liu, Z. (2024). Fractional differential equations for modeling the spread of misinformation in social networks. Journal of Complex Networks, 15(3), 227-240.

Li, Y., Liu, Y., & Zhang, J. (2025). Dynamic analysis of a fractional order SINPR rumor propagation model with emotional mechanisms. Fractal and Fractional, 9(8), 546.

Wang, H., & Xu, S. (2024). A fractional order model for misinformation spread on digital platforms. Nonlinear Dynamics, 55(6), 815-829.

Wang, L., Zhang, M., & Li, X. (2023). Fractional epidemic models with memory: A case study on misinformation spread. Applied Mathematical Modelling, 49(7), 1230-1245.

Yamada, T. (2023). Influence of fractional derivatives in social contagion and misinformation modeling. International Journal of Computational Mathematics, 30(2), 124–139.

Yue, X., & Zhu, W. (2024). The dynamics and control of an ISCRM fractional order rumor propagation model containing media reports. AIMS Mathematics, 9(4), 9721–9745.

Zhang, J., Zhao, F., & Tan, S. (2024). Modeling misinformation spread using fractional calculus: Application to online social media. Journal of Computational Physics, 22(9), 1120-1132.

Zhang, L., & Tan, L. (2023). Long term memory and delay effects in the spread of misinformation: A fractional order approach. Journal of Mathematical Sociology, 47(6), 243-256.

Xu, X., & Wu, Y. (2024). Fractional epidemic models for misinformation spread in large-scale networks. Journal of Complexity, 61, 301-315.

Kang, W., & Zhou, Y. (2023). Nonlinear dynamical systems for modeling misinformation with fractional derivatives. Chaos, Solitons & Fractals, 157, 112241.

Wu, Z., & Luo, T. (2023). The effect of media influence on misinformation spread: A fractional approach. Mathematical Methods in the Applied Sciences, 32(1), 212-221.

Huang, Q., & Jiang, T. (2024). Fractional SIR model with memory for rumor propagation. Journal of Computational Mathematics, 32(6), 415-430.

Zhou, L., & Wang, Q. (2024). Modeling misinformation spread with non-local interactions using fractional differential equations. Nonlinear Analysis: Real World Applications, 65, 102489.

Li, H., & Zhao, G. (2025). Fractional modeling and its application in misinformation diffusion dynamics. Computational and Applied Mathematics, 44(3), 412-429.

Sun, Y., & Zhang, Z. (2024). A new fractional model for online misinformation spread: Applications and analysis. Discrete & Continuous Dynamical Systems Series B, 29(8), 3765–3779.

Liu, W., & Zhang, H. (2023). Effects of memory on rumor spread in social networks: A fractional derivative approach. Physica A: Statistical Mechanics and its Applications, 587, 126407.

Qiu, Y., & Zhang, Y. (2023). Fractional order Susceptible-Infected-Recovered model for misinformation propagation. Journal of Applied Mathematics, 20(7), 855-868.

Bai, X., & Li, T. (2024). Fractional order models of misinformation: Investigating the role of delayed information propagation. Mathematical Modelling of Natural Phenomena, 19(4), 53–67.

Fan, W., & Tang, X. (2024). Memory and long-range dependencies in misinformation spread: A fractional order approach. Physica D: Nonlinear Phenomena, 422, 132758.

Li, Y., Liu, Y., & Zhang, J. (2025). Dynamic analysis of a fractional order SINPR rumor propagation model with emotional mechanisms. Fractal and Fractional, 9(8), 546.

Wang, H., & Xu, S. (2024). A fractional order model for misinformation spread on digital platforms. Nonlinear Dynamics, 55(6), 815-829.

Yamada, T. (2023). Influence of fractional derivatives in social contagion and misinformation modeling. International Journal of Computational Mathematics, 30(2), 124–139.

Zhou, L., & Wang, Q. (2024). Modeling misinformation spread with non-local interactions using fractional differential equations. Nonlinear Analysis: Real World Applications, 65, 102489.

Zhang, L., Zhao, F., & Tan, S. (2023). Modeling misinformation spread using fractional calculus: Application to online social media. Journal of Computational Physics, 22(9), 1120-1132.