Optimal control of chemotherapy of HIV model using the coupled Adomian/Alienor methods

Abstract

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.

On comparison between iterative methods for solving nonlinear optimal control problems

“…It is known that a nonlinear optimal control problem (OCP) can be converted to a Hamilton-Jacobi-Bellman (HJB) partial differential equation or a nonlinear two-point boundary value problem (TPBVP). Many researchers have attempted to solve these two problems (see Diehl et al, 2005;Fakharian and Behshti, 2008;Fakharian et al, 2010;Fakharzadeh, 2012;Ha¨ma¨la¨inen and Halme, 1976;Jajarmi et al, 2011;Manseur et al, 2005;Matinfar and Saeidy, 2014;Nik et al, 2012, and the references therein).…”

“…Fakharian et al used the modified Adomian decomposition method (ADM) (Fakharian and Behshti, 2008;Fakharian et al, 2010), Saberi Nik et al applied the homotopy perturbation method (HPM) (Nik et al, 2012), Jajarmi et al used the series method (Jajarmi et al, 2011), Manseur et al applied the coupled Adomian/Alienor method (Manseur et al, 2005), Fakharzadeh used differential transformation method (DTM) (Fakharzadeh, 2012) s:t:…”