The spread of rumors has an important impact on the production and life of human society. Moreover, in the process of rumor propagation, individuals with different educational levels show different degrees of trust and ability to spread rumors. Therefore, a new rumor propagation model was established, which considers the influence of education level on rumor propagation. Initially, the basic reproduction number of the model was calculated. Then, we analyzed the existence and stability of the rumor equilibrium point. Next, based on the principle of Pontryagin's maximum value, we obtained a control strategy, which effectively reduced the spread of rumors. Numerical simulations verified the results of theoretical analysis. The results showed that the higher the education level of the population, the slower the spread of rumors to a certain extent, but it could not prevent the spread of rumors. In addition, through the support of the government and the propaganda of the official media, strengthening education can improve people's education level to a certain extent, and then minimize the speed of rumor propagation.

In the 2016 US presidential election, the widespread propagation of false news on social media, especially rumors against Hillary Clinton, quickly affected the emotions and decisions of some voters, highlighting the potential impact of rumors on voters' perceptions and election results. An individual's ability to identify rumor information determines their tendency to judge and spread rumors, thus directly affecting the spread of rumors and society's trust in information. Considering the impact of individual identification ability on rumor propagation, this paper established a new rumor propagation model, calculated the basic reproductive number of the model, and proved the existence of equilibrium points in the model as well as their local and global asymptotic stability. Meanwhile, based on Pontryagin's maximum principle, we chose the probability of contact between ignorant individuals and rumor spreaders, the probability of conversion of spreaders into immunized individuals, and the contact rate between rumor spreaders and truth spreaders as the optimal control variables, and obtained an effective strategy for reducing rumor spreading. The numerical simulation verified the results of theoretical analysis. The findings of this study suggest that enhancing individual identification ability can effectively slow down the propagation of rumors.