Bayesian fractional stochastic models for controlled release mechanisms in nanoparticle drug delivery

Optimizing drug release kinetics from nanocarriers is crucial for enhancing therapeutic efficacy and minimizing systemic toxicity in pharmaceutical formulations. Traditional deterministic models often fail to adequately capture the complex, non-Fickian diffusion and stochastic variability inherent in nanoparticle-based drug delivery systems. This study develops and applies a Bayesian fractional stochastic model to describe drug release kinetics from liposomal, polymeric, and metallic nanoparticles. The model integrates fractional calculus to account for anomalous diffusion and memory effects, while Bayesian inference enables dynamic parameter estimation under uncertainty. Experimental drug release data were obtained across varying temperature and pH conditions, with additional evaluations of nanoparticle size and initial drug concentration effects. The proposed model achieved the lowest Root Mean Squared Error (RMSE = 2.31) and optimal Bayesian Information Criterion (BIC = 35.6) compared to traditional models, including Higuchi, Korsmeyer-Peppas, Zero-Order, and Weibull models. Sensitivity analyses revealed that drug release efficiency increased with temperature, lower pH, smaller nanoparticle size, and higher initial drug concentration. The Bayesian approach enabled real-time updating of fractional order (a) and release rate constant (k), ensuring model adaptability under varying experimental conditions. These findings confirm that the Bayesian fractional stochastic model provides a robust, adaptive, and accurate predictive tool for optimizing drug release from nanoparticle systems. This approach holds substantial potential for guiding the rational design of next-generation, patient-specific drug delivery systems in nanomedicine.