Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes

In this paper, an SIR rumor propagation model is established with the three recovery modes that the spreader turns into a stifler under the influence of the spreader, stifler and media nonlinear rumor-refuting mechanism. Firstly, we calculate the basic regeneration number, and we determine the stability of the rumor-free equilibrium and the existence of the rumor-endemic equilibrium. Secondly, by applying the strict symbolic calculation methods of singular quantities, we investigate the Hopf bifurcation at the rumor-endemic equilibrium, and we determine the existence of single and double periodic solutions under certain parameter conditions. Thirdly, we discuss the practical dynamic behaviors of rumors spreading from the perspectives of the basic reproduction number and periodic solutions, especially the correlation between these two and multi-periodic oscillations. To our knowledge, such complex dynamic properties have rarely been analyzed in rumor models.