Dynamical analysis and optimal control of a Hyper-SICR rumor spreading model on hypergraphs

Rumor spreading on online social platforms often exhibits group-interaction characteristics involving multiple users. To investigate rumor spreading under higher-order interaction structures, this paper constructs a Hyper-SICR rumor-spreading model based on hypergraph theory and introduces the single-contact transmission probability and saturated incidence rate. First, the basic reproduction number \(R_0\) of the model is derived, and the existence and stability of the rumor-free equilibrium and rumor-prevailing equilibrium are analyzed. Numerical results provide support for the theoretical analysis. Comparison with the degenerated SICR model shows that, under the same parameter conditions, the higher-order structure leads to a lower \(R_0\) . After further matching the same \(R_0\) , effective growth rate, and decay rate, dynamical differences between the two models still remain, further reflecting the influence of the higher-order structure on the system dynamics. Finally, an optimal control model is constructed. Numerical results show that the optimal control can adjust the control intensity according to different hyperdegrees, and larger hyperdegrees require stronger early-stage control. Under the same total cumulative cost, the optimal control achieves a better suppression effect than uniform control.