Investigation into hate speech dissemination dynamics in a community using fractional order modeling approach

Abstract

The dissemination of hate speech 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 dissemination of hate speech, as an evolutionary system. The non-negativity and boundedness of the solutions of the fractional order model have been shown to make the evolutionary system meaningful. Both the 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 effective reproduction number of the hate speech model is less than unity. The global asymptotic stability of the hate speech-persistent equilibrium point has also been shown. Moreover, we employed Pontryagin's Maximum Principle to determine the optimality conditions of the optimal control problem, performed sensitivity analysis on the model parameters, and conducted numerical simulations using MATLAB's ode45 solver in combination with Euler's forward and backward numerical methods. This enabled us to investigate the effects of order of the fractional derivative and the proposed strategies on the behavior of responses of the model. Implementing protection and treatment strategies against hate speech dissemination has a significant effect on disrupting and counteracting the propagation of hate speeches within a community, as evidenced by the graphical representation of the numerical simulation.