In this paper we propose several new mathematical models for estimating effective diffusivities of a drug released from a cylinder device to an external finite volume. These models can handle problems with ‘initial burst’ and boundary layers. Analytical solutions to the models are derived. To determine the unknown effective diffusivity, time of a initial burst and width of the effective boundary layer, a least-squares method can be used for a given experimental data set. The models were tested using experimental data and the numerical results show the usefulness and accuracy of these models.