International Journal of Mathematics and Statistics Studies (IJMSS)

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Drug Diffusion from the Gastrointestinal Tract through the Body, Bloodstream, and Urinary Compartments: Mathematical Modeling Approach


This research involved the formulation of a mathematical system that mimics the diffusion of drug concentration from the gastrointestinal tract to the body and bloodstream compartments and the elimination through the urinary tract. The models are formulated separately as ordinary differential equations for the aforementioned compartments, where some pertinent entry parameters in the form of rates were obtained. We applied the Laplace method of solution to solve the formulated mathematical models for the drug concentration in the various compartments as mentioned. In order to investigate the effect of the drug concentration in the urinary and gastrointestinal tracts on the concentration in the body and bloodstream compartments, we solved the urinary tract and gastrointestinal models and substituted the results into the models representing the drug concentration in the body and bloodstream compartments, and those models were later solved to obtain the function representing the body and bloodstream compartments. The research further involved the numerical simulation of the various functions obtained by varying the various rates of diffusion on the drug concentration in the body and bloodstream compartments. The results revealed that the various diffusion rate changes affect the drug concentration level in the body and bloodstream compartments, respectively. The novelty of this research is the fact that we’ve been able to incorporate drug administration and concretion in the gastrointestinal and urinary tracts, which were not considered previously. This research is recommended for application by mathematicians and scientists alike who could be interested in understanding drug diffusion from one compartment to another with different rate constants.

Keywords: Body, Diffusion, Drug, Gastrointestinal tract, bloodstream, mathematical modeling, urinary and compartment diagram

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