Abstract: With the increasing popularity of the Internet and the spread of COVID-19, epidemic-related rumors have attracted significant attention, allowing them to brew quickly and pose extremely negative social impacts. It is of great significance to investigate the propagation process of online rumors and offer tentative strategies to curb it. Based on the traditional susceptible, infected, recovered (SIR) model of online rumor propagation, groups of potential and die-hard rumor believers were introduced in this paper, establishing an authoritative rumor-refuting mechanism. Meanwhile, this paper considered factors such as the time-lag effect of rumor refutation from the nonauthoritative and authoritative institutions and the impact of the popularizing rate of higher education on the propagation and refutation of rumors. As a result of the process, the SEIRD (susceptible, exposed, infected, recovered, die-hard-infected) rumor propagation model was established to study how the proportion of the susceptible, exposed, infected, recovered, and die-hard-infected varies under different popularizing rates of higher education, the presence or absence of the authoritative rumor-refuting institutions, and the time-lag effect of rumor refutation. Finally, the model’s effectiveness was verified via experimental simulation, which provided a reference for controlling the spread of online rumor propagation. In addition, the paper proposed a rumor-refuting coefficient to measure the rumor-refuting ability of the nonauthoritative and authoritative institutions. The results show that (1) increasing popularizing rate of higher education significantly slows down the rumor propagation and reduces the rumor propagation peak; (2) refuting the rumors based on the authoritative institutions is decisive for the ultimate elimination of rumors; and (3) eliminating the time-lag effect in refuting rumors facilitates slowing down the propagation of the online rumors. Therefore, the paper puts forward a feasible strategy to eliminate the time-lag effect of online rumor refutation in the future.