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, R0. Using the Lyapunov direct method, the global stability of each equilibrium is proven to depend primarily on R0. Theoretical findings are validated through numerical simulations, exploring the impact of vaccination and fractional derivatives on the epidemic dynamics.