Differential Equations Modelling of Drug Absorption and Elimination in Pharmacokinetics

This study applies systems of ordinary differential equations to model the pharmacokinetic processes of drug absorption, distribution, metabolism, and elimination in the human body, with illustrative parameters drawn from clinical data relevant to therapeutic agents commonly prescribed in Nigerian public health facilities. Pharmacokinetics provides the quantitative biological framework for understanding how drug concentration in the body evolves over time following administration, and its mathematical modelling has direct implications for dosing regimen design and therapeutic monitoring. The study develops one-compartment and two-compartment pharmacokinetic models formulated as systems of first-order linear differential equations, and obtains analytical solutions using Laplace transform methods and eigenvalue decomposition. Model parameters including absorption rate constants, elimination rate constants, and volume of distribution are estimated from published clinical pharmacokinetics literature for antimalarial drugs, antihypertensive agents, and antibiotics commonly used in Nigerian clinical practice. Simulation studies are conducted to visualise concentration-time profiles under single-dose and multiple-dose regimens, and minimum effective concentration and toxic concentration thresholds are incorporated into the simulations. The study evaluates how patient-specific factors including body weight, renal function, and bioavailability variability affect predicted plasma concentrations. Results highlight scenarios in which standard dosing regimens may produce subtherapeutic concentrations in certain patient subgroups. Keywords: pharmacokinetics, differential equations, drug absorption, compartment models, therapeutic dosing