Rumor spreading in OSNs has been posing a significant threat to maintain the normal social order. In recent years, extensive efforts have been directed towards studying the rumor dynamics based on epidemic models, assuming that only the rumor cascades exist in the network for a specific event. In this paper, a novel rumor spreading model called ILRDS is proposed to describe the rumor dynamics in OSNs under emergencies. Different from previous studies, the model considers that when an ignorant is exposed to a rumor or counter-rumor, he or she will change into a latent with one of three different attitudes toward the rumor. Furthermore, the influence of debunking behavior and varying total population on the rumor dynamics are also investigated in this paper. Then, the stability of ILRDS model is analyzed by using the Lyapunov function-based method and Poincarè–Bendixson property. Finally, simulations are carried out to describe the influence of different parameters on the rumor spreading process, and the corresponding management strategies for restraining the rumor spreading under the emergencies are also discussed in this paper.