Mathematical modeling of drug delivery systems with diffusion and absorption equations

Mathematical modelling plays a fundamental role in designing drug delivery systems, where the goal is to release an active molecule at a controlled rate and in a specific target region. Diffusion and absorption processes govern how drugs migrate through polymers and tissues and how they are taken up by the body. Challenges arise from spatially varying material properties, nonlinear boundary conditions and the coupling between diffusion within the device and absorption by biological tissues. This paper formulates a one dimensional diffusion–absorption model for a controlled‐release reservoir coupled to a sink that mimics systemic uptake. Starting from Fick’s laws, we derive the governing partial differential equation with a first order absorption term and solve it using separation of variables and Laplace transforms. The model predicts concentration profiles inside the device and the fraction of drug released as functions of time. Results show that higher diffusion coefficients accelerate release, whereas stronger absorption reduces internal concentrations but increases the rate of systemic delivery. The proposed framework provides insights into the interplay between device parameters and pharmacokinetic outcomes and offers guidelines for optimizing controlled release formulations.