PurposeThe purpose of this paper is to show that a combination of Adomian and Alienor methods can be used to solve the problem of parameters identification of HIV/AIDS model. This model involves a system of three ordinary differential equations.Design/methodology/approachParameters identification leads to the minimization of an error functional given by the sum of variations between measured variables and calculated variables obtained by solving the system of differential equations. We assume that the quantity of healthy cells CD4 + T and the viral load contents in the blood are measured.FindingsThe identification was realized by applying the combined Adomian/Alienor method allowing to reduce the problem to a minimization problem in dimention one.Practical implicationsSimulation results are given for illustration.Originality/valueApplication to parameter identification in an HIV model‐compatible, results to other methods.

PurposeThis paper aims at applying the proven Adomian and Alienor methods to solve the problem of optimal chemotherapy of HIV model.Design/methodology/approachThe combination of the Adomian decomposition method and the Alienor reduction method allows us to solve the control problem as if it were a classical one‐dimensional minimization problem. The methodology is applied to a HIV model and simulation results given.FindingsA general abstract framework for the control of a non‐linear evolution system has been developed. It was shown that it is possible to control a system by using the powerful techniques of Adomian and Alienor, and produce results comparable with those obtained by classical methods where other cost functions are used.Research limitations/implicationsThe benefit of this work is based on the CD4 healthy cells being maximized and the cost based on a drug dose being minimized. The new methodology could be used after further research for solving many control problems in biology and in other areas such as those involving industrial processes.Practical implicationsNew methodology is cost‐effective in controlling the drug dose affecting rate of infection of cells by HIV virus.Originality/valueNew application of proven methodology will solve many control problems in biocybernetics/biomedicine/industry and other fields.

PurposeAims to propose methodology to solve adaptive control problems by the use of the Adomian decomposition method (ADM).Design/methodology/approachThe approach to this problem is through the ADM which consists in finding a solution of nonlinear state equations as a convergent series that depends on the unknown parameters of the system.FindingsIt was shown that a first approach for solving adaptive control problems could be tackled by using the ADM. The solution of the systems was obtained in a series forms as a function of the unknown parameters. The objective function became a function that explicitly depends on parameters. This, it was shown, can be minimised by classical or nonclassical global optimization methods.Research limitations/implicationsThe methods presented depends on ADM. It is proposed that future work involves the study of an adaptive control problem associated to a nonlinear compartmental systems of Michaels‐Menten type.Originality/valuePresents an applications of the developed ADM using it, as adapted to control problems. It contributes to mathematical modelling studied concerning most biological, physical phenomena which are described by nonlinear systems: differential, partial differential in form and for which there is little hope of finding an exact solution.

Purpose -In this paper, non-linear compartment modelling is used to study drug transport of anticancerous substance across brain tissues. The aim of the work is to identify the pharmacokinetic parameters of the model created. Design/methodology/approach -A combination of the Adomian decomposition method and the Alienor reducing transformation method were used to solve the identification problem as if it were a classical one-dimensional minimization problem. Findings -The numerical results using this methodology have shown that local therapeutic method should be preferred, when it comes to evaluate the rate (of healthy cells/cancerous cells), especially when, somehow, the drug transition into the tumour is speeded up. The combination method of Adomian and Alienor proved a successful strategy, and could take into account many of the pharmacokinetic parameters as necessary and use well-known algorithms. Research limitations/implications -It is believed that this modest work can be considered as preliminary steps for improving local drug administration. Practical implications -The study has shown that pharmacokinetic/pharmacodynamic modelling can help to understand the drug behaviour in such complex media and hence avoid the most threatening side effects by predicting the toxicity threshold of a drug and therefore minimize the therapeutic index. Originality/value -Shows the powerful tools of Adomian and Alienor techniques that can be applied successfully in biomedical applications.

PurposeThis paper deals with the use of the combined Adomian/Alienor methods for solving the problem of optimal cancer chemotherapy model.Design/methodology/approachThe combination of the Adomian decomposition method and the Alienor reducing transformation method allows us to solve the control problem as if it were a classical one dimensional minimization problem. The mathematical model used here describes specific model based on cell‐cycle kinetics.FindingsIt was found that the goal is to maintain the number of the cancerous cells around a desired value while keeping the toxicity to the normal tissues acceptable.Practical implicationsSimulation results are given for illustration.Originality/valueNew combined approach to optimal control of cancer chemotherapy using Adomian/Alienor Methods.