In this paper, based on the transmission mechanism of measles virus, considered the memory effect of virus transmission, a class of fractional-order SVEIR infectious disease model with fear effect and secondary vaccination is established, and the effects of fear factor and secondary vaccination rate on controlling the infectious disease are studied. The basic reproduction number \(R_0\) and the positive invariant set of the model are obtained by calculation, and the existence and uniqueness of solutions are analyzed. By using the fractional-order eigenvalue method and Lyapunov function, sufficient conditions for the stability of equilibrium points under threshold conditions are derived. Finally, through sensitivity analysis and numerical simulation, the Hopf bifurcation’s conditions to occur are obtained by using the transmission rate \(\beta \) and the fractional order \(\alpha \) as the bifurcation parameters, and the influence of different fractional orders is portrayed. The results indicate that changes in the fractional order \(\alpha \) affect the system’s stability and convergence speed. It is obtained that the increase of the fear factor and the rate of the secondary vaccination can reduce the basic reproduction number and control the spread of the disease. Additionally, simulations using the number of measles cases in China in 2023 indicated that \(\alpha = 0.73\) better fits the data.
