Analysis of a fractional endemic SEIR model with vaccination and time delay

This article analyzes a fractional-order SEIR infection epidemic model, including time delays and vaccination strategies. Four differential equations describe the infection dynamics with non-integer derivative orders, which account for memory effects and non-local interactions in disease spread. The paper first establishes the existence and uniqueness of the solution and presents equilibrium points based on the basic reproduction number, \(R_{0}\). Using the Lyapunov direct method, the global stability of each equilibrium is proven to depend primarily on \(R_{0}\). Theoretical findings are validated through numerical simulations, exploring the impact of vaccination and fractional derivatives on the epidemic dynamics.