Modeling and Analysis of Hate speech Propagation in a Community using Fractional Order Derivatives

Abstract The propagation of hate speech directed toward local public sector administrations in a community has become an issue of great concern. Hate speech not only undermines social harmony but also poses significant challenges to the smooth functioning of the public sector and the well-being of the community members. In this study, we formulated and analyzed a Caputo fractional order model with optimal control strategies on the propagation of hate speech, as an evolutionary system. The non-negativity and boundedness of the solutions of the fractional order model have been shown with the objective of making the evolutionary system meaningful. Both hate speech-free and hate speech-persistent equilibrium points were determined. Conditions for the backward bifurcation of the fractional order model were analyzed when the hate speech effective reproduction number is less than unity. The global asymptotic stability of hate speech-persistent equilibrium point has also been shown. Furthermore, we employed optimal control strategies and numerical simulations to examine the memory effect of the fractional order and the behavior of responses of the model. Protection and treatment of individuals engaged in propagating hate speech in the community has a significant impact in reducing and possibly exterminating hate speech propagation in the community.