An Improved ISCR Model for Rumor Propagation on Social Networks: Dynamics, Reproduction Number, and Intervention Strategies

Abstract

Rumor diffusion on online social networks (OSNs) is a fast, non-linear and high-impact phenomenon that increasingly threatens public order. We extend the classical SEIR epidemic framework to a four-compartment Improved ISCR (Ignorant–Hesitant–Spreader–Stifler) model that explicitly distinguishes the cognitive hesitation stage and incorporates an official intervention intensity u. Specializing to constant control we derive, via the next-generation matrix method, a closed-form effective reproduction number , which yields an interpretable threshold  for rumor extinction. We complement the mean-field analysis with agent-based simulations on Barabási–Albert (BA) scale-free and Watts–Strogatz (WS) small-world networks, run on 5 independently generated graphs  6 random seeds (n=30 per configuration) and extended until  to avoid endpoint censoring. We benchmark five governance policies including a novel combined early-intervention plus opinion-leader-immunization rule. Results show that (i) on BA networks, random immunization is essentially inefficient (76.7%→74.7%); opinion-leader immunization alone reduces final reach to 17.5 14.3%; the combined policy further compresses it to  under the same 5% immunization budget jointly with early control; (ii) topology-effect claims are robust: under random-seed initialization the BA reach drops to 45.7% but remains higher than WS’s 14.5%, while hub-seeded BA still dominates; (iii) the joint policy is the only one that simultaneously achieves low mean and low variance, which is critical for governance reliability.