In this paper, we investigate a time-fractional singularly perturbed reaction-diffusion equation with delay, which arises in various applications of disease modelling and control theory. The model incorporates a Caputo fractional derivative of order \(\alpha \in (0,1)\) to account for memory effects, a small diffusion parameter \(\varepsilon \) that induces multiscale behaviour, and a delay term representing incubation or feedback lag. Such features make the problem analytically and numerically challenging. A uniform mesh is used to discretize the time domain and a piecewise uniform Shishkin mesh is employed to discretize the spatial domain. The proposed numerical approach consists of \(L1-2\) scheme in time direction and a fourth order compact finite difference (CFD) scheme is used in the space direction. Error estimates are established, demonstrating that the scheme is parameter uniform convergent and achieves accuracy of order \(O(\Delta t^{3-\alpha } + N^{-4}(\ln N)^4)\) . Numerical experiments are presented to confirm the theoretical findings and to illustrate the effectiveness of the proposed scheme in capturing the solution behaviour, including possible boundary layer phenomena. The results indicate that the developed numerical approach provides a reliable and efficient computational framework for solving time-fractional singularly perturbed reaction-diffusion problems with delay arising in biological and controlled dynamical systems
