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AbstractPurpose -To show how the combined Adomian/Alienor methods for solving adaptive control problems can successfully be applied to chemotherapy. Design/methodology/approach -Problem formulation is first developed and combined mathematical methods (Adomian/Alienor) are used for the solution of non-linear differential equations/systems with unknown parameters and without discretization or linearization. The approach is applied to biological systems and in particular the drug/tumour two compartment model is addressed. Findings -A general abstract framework for the identification and the control of a non-linear evolution system has been developed. It was found that it is possible to identify and control a system using a powerful technique based on a combination of the Adomian/Alienor methods. This produced a methodology which showed its superiority over the traditional methods in that as a result of their implementation we can predict and optimize the individual dosage in the described application.Research limitations/implications -The combined techniques proved to be successful for the optimization of drug administration where account is taken of effectiveness, usefulness and safety. Further research collaboration between multidisciplinary scientists and practitioners directed towards more insight into drug/cancerous cells behaviour is required. Practical implications -An alternative to other classical techniques to solve control/identification problems has been produced. Originality/value -New combined technique given which is superior to traditional ones for certain therapeutic cases.
IntroductionIn biological systems, we usually have a poor or incomplete understanding of the phenomenon under consideration. Our aim is to make a contribution to the science of drug delivery into a living body. We believe that a mathematical model is the best way to describe the behaviour of a biological complex system with different processes occurring simultaneously (non-linearity, elimination, metabolism, etc.), that cannot be explained in other ways. The mathematical modelling of such a phenomenon leads to a system of non-linear differential equations with unknown parameters that must be controlled...
