This study designs the Morlet wavelet neural network (MWNN) for the numerical performance of the second-order delay differential perturbed singular model (DD-PSM). These stiff singular models are always challenging for the research community to numerically present their results. The DD-PSM is used as an objective function, and its boundary conditions are assembled and then optimised using the computing hybrid proficiency of the global genetic algorithm (GA) and local active-set approach (ASA). Details of the singularity, shape factor, perturbed and delay terms based on the DD-PSM are also provided. Three problems of the DD-PSM are presented and numerically solved using the MWNN–GA–ASA. The precision of the MWNN–GA–ASA is studied by comparing the proposed solution-based DD-PSM and exact solutions. Moreover, a comparison of the MWNN with the Meyer wavelet neural network is presented. The reliability, convergence, correctness and constancy of the numerical scheme are observed by different statistical performances.