Semi-Analytical Treatment of a Coupled Advection–Diffusion–Reaction System for Spatiotemporal Drug Therapy Modeling via the Triple Laplace Transform and Adomian Decomposition

Abstract

This research presents an approximate method for solving a

medical application system using the concept of load, diffusion, and

interaction, where the system depicts the concentrations of the drug,

diseased cells, and healthy cells in a given tissue. Inspired by biology,

this approach utilizes the triple Laplace transform to convert the problem

into an algebraic form within the transformation domain. Nonlinear limits

are handled using the Adomian formula, an iterative method that allows

for the construction of a solution sequence. After obtaining the general

load formula, three arbitrary cases of functions that satisfy the system

without residues are selected for numerical testing. The results

demonstrate the validity of the method as a tool for generating solution

formulas for medical systems, provided a precise solution is available.