A Fractional‐Order Model for Rumor Propagation: Role of Government Surveillance and Deactivation of Social Media Accounts

ABSTRACT This paper introduces a fractional‐order model for rumor propagation that takes into account government surveillance and the deactivation of social media accounts of users spreading rumors. The equilibria of the model are calculated, and stability analysis is carried out based on the basic reproduction number . The model shows a backward bifurcation, indicating that having less than 1 is insufficient to eliminate the rumor from the population. It is necessary to reduce below a certain threshold, , for effective rumor control. Further, we have discussed the Hopf bifurcation phenomenon considering the government surveillance parameter (rate of deactivating social media accounts of users spreading rumors) and the fractional order as bifurcation parameters. As is independent of the government surveillance parameter , variations in the value of do not influence . Nonetheless, an increase in the value of leads to a decrease in rumor propagation. The threshold value of the parameter is given to eliminate and control the rumor from the population.