Rumors in social systems are omnipresent. While traditional models focus on pairwise interactions, the collective effects of group interactions are insufficiently explored. Here we present a rumor propagation model on higher-order networks that incorporates 2-simplex structures and adaptive transitions between active and passive individuals. We find that higher-order networks substantially lower the propagation threshold and intensify nonlinear spreading effects. Active individuals are key drivers of rumor propagation and persistence. With active contagion, we observe that higher-order propagation increases peak and steady-state densities of active spreaders, thus extending the propagation and lifespan of rumors. We also apply a sequential quadratic programming algorithm to optimize the parameters of our model and validate its accuracy and applicability on real-world data. These results advance our understanding of contagion in higher-order social networks and support the design of targeted strategies for rumor mitigation.

Rumor is an important form of social interaction, and its spreading has a significant impact on human lives. In this paper, a rumor propagation model with latent period and varying population is considered, which assumes an ignorant individual first goes through a latent period after infection before becoming a spreader or a stifler. Agents that read the rumor but have not decided to spread it, stay in the latent period. By means of the Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the rumor-free equilibrium and the rumor-endemic equilibrium by using the Poincarè-Bendixson property. Then an optimal control problem is formulated, from the perspective of a manager in emergency events, to maximize positive social effects with rumor spreading when the emergency resources are under constraints. Control signals, such as science education and official medial coverage attempt to convert lurkers and spreaders into stiflers. By employing Pontryagin’s maximum principle, the optimal solution is acquired when the emergency response incurs nonlinear costs. Finally, we outline some strategies for managers that can contribute to rumor control in an emergency event.

This paper considers a rumor transmission model with incubation that incorporates constant recruitment and has infectious force in the latent period and infected period. By carrying out a global analysis of the model and studying the stability of the rumor‐free equilibrium and the rumor‐endemic equilibrium, we use the geometric approach for ordinary differential equations which is based on the use of higher‐order generalization of Bendixson’s criterion. It shows that either the number of rumor infective individuals tends to zero as time evolves or the rumor persists. We prove that the transcritical bifurcation occurs at R₀ crosses the bifurcation threshold R₀ = 1 by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function of R₀, as a consequence for successful eradication of the rumor, one should simply reduce R₀ continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.