With the development of the Internet and the spread of COVID-19, the attention of epidemic-related rumors has greatly increased, allowing them to quickly brew and pose extremely negative social impacts. It can be seen that it is of great significance to conduct the research into the propagation process of online rumors and try to offer tentative strategies to curb it. Based on the traditional SIR(susceptible, infected, recovered) model of online rumor propagation, groups of potential rumor believers and die-hard rumor believers are added into this paper, which introduces the authoritative rumor-refuting mechanism. Meanwhile, the paper also takes such factors into consideration as the time-lag effect of rumor-refuting from the non-authoritative and the authoritative, as well as the impact of the popularizing rate of higher education to their propagation and refutation. As a result of the process, the SEIRD(susceptible, exposed, infected, recovered, die-hard-infected) rumor propagation model was established to research how the proportion alters, of the susceptible, the exposed, the infected, the recovered and the die-hard-infected, under different popularizing rate of higher education, and the presence or absence of the authoritative rumor-refuting information and the time-lag effect of rumor-refuting. Finally, the effectiveness of the model is verified by experimental simulation, which provides a reference for controlling the spread of online rumor propagation. In addition, the paper proposes the rumor-refuting coefficient to measure the rumor-refuting capacity of the non-authoritative and the authoritative, and gives its algorithm design. The research results show that increasing the popularizing rate of higher education has a significant effect on slowing down the propagation of rumors and reducing the peak of rumor propagation; refuting the rumors from the authoritative is decisive for the ultimate elimination of rumors; eliminating the time-lag effect in refuting rumors is also of great help to slowing down the propagation of online rumors. For this reason, the paper also puts forward a feasible strategy to eliminate the time-lag effect of online rumor-refuting in the future.