Mathematical Modeling of Time-Dependent Concentration of Alcohol in the Human Bloodstream Using the Eigenvalue Method

Abstract

We have been able to mimic the time-dependent concentration of alcohol in the human blood stream and body. We started by proposing a two-compartmental mathematical model to describe and understand the alcohol dynamics in the body and bloodstream. We went further to solve the proposed model analytically using the eigenvalue method. Through numerical study of the solutions, we carried out sensitivity analysis of the model parameters k₁₂ and k₂₁ to the alcohol blood concentration as a function of time and the maximum blood alcohol concentration as a function of initial concentration for 40 hours and found out that the bloodstream attains its maximum alcohol concentration at 2 hours, 20 minutes. Lastly, we found out that while the magnitude of the maximum blood alcohol concentration increases as k₁₂ increases, it decreases as k₂₁ increases. The novelty of the project is the fact that we have been able to mimic alcohol concentration in the bloodstream and in the body using mathematical models.