Dynamic analysis and optimal control of rumor propagation models considering different education levels and hesitation mechanisms

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.