Chronic diseases usually require repetitive dosing. Depending on factors such as dosing frequency, mode of administration, and associated costs this can result in poor patient compliance. A better alternative involves using drug delivery systems to reduce the frequency of dosing and extend drug release. However, reaching the market stage is a time-consuming process. In this study, we used two numerical approaches for estimating the values of the critical parameters that govern the diffusion-controlled drug release within bilayered core-shell microspheres. Specifically, the estimated parameters include burst release, drug diffusion coefficient in two polymers, and the drug partition coefficient. Estimating these parameters provides insight for optimizing device design, guiding experimental efforts, and improving the device's effectiveness. We obtained good agreement between the models and the experimental data. The methods explored in this work apply not only to bi-layered spherical systems but can also be extended to multi-layered spherical systems.