Mathematical Modeling of Alcohol-Drug Concentration in the Bloodstream

Abstract

This research involved the formulation of a system of mathematical models mimicking alcohol concentration in the human body and in the bloodstream, which are subjected to some initial conditions. The formulation starts with the an ideal presentation of the compartment diagram in Figure 1, the figure clearly indicates the two compartment in focus and the diffusion of alcohol from one compartment to the other with different rates including the elimination rate through urination and sweating that were not considered in this research. The aim of the research is to investigate the importance of the various rate constants on the alcohol concentration in the bloodstream, as well as investigating the drug dosage and volume of alcohol concentration impact in the bloodstream. The Laplace method (LM) was adopted to solve the model which represents, firstly, the alcohol concentration in the body where an exact solution was obtained, secondly, the exact solution was also obtained for the model depicting the alcohol concentration in the bloodstream with all pertinent parameters clearly spelt out. Lastly, numerical simulation was carried out using Wolfram Mathematica, version 12, where the pertinent parameters values were varied and the results presented graphically. The graphical results indicate that the various rate constants, dosage increase and the volumetric increase have impact and showed a corresponding effect on the drug concentration in the bloodstream. The novelty of this research is the fact that we’ve been able to mimic a real-life scenario, an alcohol concentration in the bloodstream, mathematically, and solved the system using Laplace methods and performed numerical simulation to show the importance of the pertinent parameters. This system can be recommended for scientists and engineers alike who could be interested in pharmacokinetics and Pharmacodynamics research.