A multilayer mat for dispensing colistin sulfate through a body surface was prepared by electrospinning. The fabricated system comprised various polyvinyl alcohol fibrous layers prepared with or without the active ingredient. One of the electrospun layers contained water-soluble colistin sulfate and the other was prepared from the same polymer type and composition without the active drug and was finally heat-treated. The heat treatment modified the supramolecular structure and conferred the polymer nanofibre with the rate-controlling function. The microstructure of different layers was tracked by positron annihilation lifetime spectroscopy, and detailed morphological analysis of the fibre mats was performed using a scanning electron microscope. The drug-release profiles of various layer arrangements were studied in relation to their antimicrobial activity. The finite element method was applied to overcome the challenge of diffusion-controlled drug release from multilayer polymer scaffolds. The finite element method was first verified using analytical solutions for a simple arrangement (one drug-loaded swellable fibre and one rate-controlling nonswellable fibre) under perfect sink conditions and in a well-stirred finite volume. The effect of alternate layer arrangements on the drug-release profiles was also investigated to plan for controlled topical drug release from fibrous scaffolds. This design is expected to aid in increasing local effectiveness, thus reducing the systemic loading and the consequent side effects of colistin.