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\begin{document}

\title{Numerical simulation of a two compartmental fractional model in
pharmacokinetics and parameters estimation}



\author[1]{Yanli Qiao}%
\author[1]{Huanying Xu}%
\author[1]{Haitao Qi}%
\affil[1]{Shandong University}%


\vspace{-1em}



  
  \date{March 15, 2025}


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\begin{abstract}
Compartmental model is the classic and widely used approach in
pharmacokinetics. Recently, fractional calculus is introduced to
describe the time course of drugs in human body which follow the
anomalous diffusion mechanism. To consider the different fractional
order transmission process, the two compartmental fractional model has
been proposed and studied. And, it will be of great significance to find
out a simple and efficient numerical method to solve the model and
estimate model parameters. This work investigates two numerical methods
of the two compartmental fractional model using finite difference
schemes, which are based on the shifted Gr\selectlanguage{ngerman}ünwald-Letnikov approximate
formula and L1 formula, respectively. The hybrid Nelder-Mead simplex
search and particle swarm optimization, denoted as NMSS-PSO, is provided
to estimate the fractional model parameters. Comparison between the
numerical solution and the solution by the numerical inverse Laplace
transform method establishes the validity of the developed numerical
algorithms. Then, the influence of the order of fractional derivative on
the drug amount in human body is also discussed. Finally, the two
compartmental fractional model is applied to fit the amiodarone
pharmacokinetics data based on the NMSS-PSO algorithms. This work will
be of importance for the development of fractional pharmacokinetics.%
\end{abstract}\selectlanguage{ngerman}%



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