This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick's principle and law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The graphs plotted illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the graphs that the drug concentration decreases in the first compartment and gradually increases in other compartments.

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A mathematical model is proposed to study the amount of drug concentration at various regions of human dermal system. The model is based on the mechanism of transdermal drug delivery systems (TDDS) with appropriate boundary conditions. The analytical solution for such problems either does not exist or is too complicated to handle. In this paper, finite element and Crank–Nicholson methods were used to find the solution of the formulated model with greater accuracy.

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