Dynamic analysis of rumor propagation considering both hibernation and countering mechanism

The persistent challenge of controlling misinformation in digital ecosystems demands advanced modeling of rumor propagation mechanisms in real-world interventions. To address this critical gap in conventional rumor-spreading models, we propose a novel Susceptible-Infected-Countering-Hibernator-Removed (SICHR) model that incorporates platform-based refutation strategies and cognitive memory effects. This study establishes dynamical equations through mean field theory to capture rumor repeatability and hibernator memory mechanisms, while employing differential equation theory to derive the basic reproduction number [Formula: see text] and analyze the existence of equilibrium. Through rigorous application of Routh–Hurwitz criteria, Lyapunov functions, and LaSalle’s invariance principle, stability at both Rumor-Free (RFEP) and Rumor-Spreading (RSEP) equilibria is conclusively proven, with validation from simulation experiments. Experimental results demonstrate that: (1) Effective rumor-refutation strategies can significantly inhibit the rumor propagation rate. (2) The forgetting and memory mechanisms inherent within the hibernator group prolong the rumor propagation cycle and delay the time required for the infected population density to reach its peak. (3) Sensitivity analysis indicates that the basic reproduction number [Formula: see text] exhibits significant hypersensitivity to hibernation and memory reactivation rates. This model aligns more closely with the empirical patterns observed in real-world rumor dissemination and has significant practical implications.