A novel approach for fractional pharmacokinetics modeling and integrating stochastic simulation techniques using Sibuya distribution

Fractional compartment models are widely used to simulate pharmacokinetics with power-law behavior. In this work, we study an approach, previously mainly used in Epidemiology for the age model, employing the Sibuya distribution, a discrete-time, non-Markov probability distribution, to effectively emulate Mittag-Leffler functions. We demonstrate the validity of our method by applying it to various pharmacokinetic datasets and comparing the results with traditional methods like the Numerical Inverse Laplace Transform (NILT) algorithm. Additionally, we propose two stochastic simulation algorithms, where the Monte Carlo SSA allows us to capture the randomness of data and the Gillespie-like stochastic numerical simulation technique can optimize computational resources in fractional analysis. • Novel Sibuya-based method solves fractional compartments with power-law dynamics. • Model precisely fits diverse drug data, showing wide applicability. • Innovative stochastic algorithms for fractional compartment model. • Stochastic methods unveil insights into pharmacokinetic chaos and outlier detection. • Potential applicability to broad scientific use in fractional analysis.