Dynamic analysis of rumor propagation model with distributed delay and saturation cure rate in multilingual environment

This study advances existing literature by proposing a novel rumor propagation model, which systematically investigates dynamical behaviors and corresponding control strategies. Explicitly tailored to the multilingual social network context, the model incorporates continuous distributed time delays and partitions the population into four distinct subgroups, thereby elucidating the underlying dynamical behaviors and mechanisms governing rumor dissemination. Through analysis of the models equilibrium points, this research derives necessary conditions for rumor extinction and establishes criteria for both local and global asymptotic stability of the rumor-free equilibrium, as well as for the rumor-prevalent equilibrium under specific parametric regimes. Additionally, it uncovers the occurrence of backward bifurcation in heterogeneous networks and develops criteria to determine its direction. Furthermore, an optimal control strategy is formulated using optimal control theory to mitigate rumor spread. Finally, numerical simulations validate the theoretical findings, laying a foundational framework for the investigation, mitigation, and management of rumor propagation in multilingual environments.