<p>This paper investigates a temporal fractional SEIR model formulated through a system of reaction–diffusion equations. The model incorporates switching cases of Neumann boundary conditions depending on the threshold of infected individuals, which are known as Signorini boundary conditions. The evolution is governed by the Caputo fractional derivative, introducing memory effects into the system dynamics. This leads to nonlinear time-dependent variational inequalities with memory, prescribing the evolution of the disease in a bounded region. We derive the variational formulation of the problem and establish the existence, uniqueness, positivity, and regularity of the solution. Building on this theoretical foundation, an L1 time discretization scheme is developed and analyzed, with rigorous results confirming its convergence and stability. Subsequently, the finite element method is employed to approximate the model’s dynamics, and its convergence along with the corresponding convergence order are rigorously established. Additionally, the study utilizes an Uzawa block relaxation algorithm to solve the system efficiently. Numerical simulations examine several scenarios, highlighting the model’s behaviour under different epidemiological conditions.</p>