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Abstract

This paper provides a considerably efficient numerical approach to acquire the solutions of a biomathematical model administrating oral and intravenous distribution of pharmaceuticals in the human body. The proposed numerical approach based on an artificial neural network is employed to extract numerical solutions for a detailed set of ordinary differential equations and analyze the change in concentration of drug diffusion via the compartments of blood and tissue medium. We primarily focus on analyzing three different models established on the diffusion process, exercising laws of mass action and Fick’s principle. In this work, the existing model is reformulated as an optimization problem by investigating the drug distribution impacted by multiple factors related to the human body. Based on the drug efficacy, the rate constants (governing the law of mass action) are applied at different interfaces. The posed optimization problem is then solved by minimizing the concerned loss function. Also, all the attached numerical parameters have been considered while computing the drug concentration within distinct compartments. In addition, with the aid of Python programming, the presented plots show how the medication concentration changes over time. The obtained graphical results signify that the rate of change in the concentration of drugs rises gradually in other compartments while decreasing in the first. Compared to the traditional methods, the experimental results demonstrate the accuracy and efficacy of the proposed methodology evidently.

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