Abstract
We present a delayed optimal control which describes the interaction of the immune system with the human immunodeficiency virus (HIV) and CD4+ T-cells. In order to improve the therapies, treatment and the intracellular delays are incorporated into the model. The optimal control in this model represents the efficiency of drug treatment in preventing viral production and new infections. The optimal pair of control and trajectories of this nonlinear delay system with quadratic cost functional is obtained by Fourier series approximation. The method is based on expanding time varying functions in the nonlinear delay system into their Fourier series with unknown coefficients. Using operational matrices for integration, product, and delay, the problem is reduced to a set of nonlinear algebraic equations.
Highlights
Delays occur frequently in biological, chemical, electronic, and transportation systems [1]
Many mathematical models have been developed in order to understand the dynamics of human immunodeficiency virus (HIV) infection [2,3,4,5,6,7]
We consider the mathematical model of HIV infection with intracellular delay presented in [15] in order to make the model more tangible and closer to what happens in reality
Summary
Delays occur frequently in biological, chemical, electronic, and transportation systems [1]. Optimal control methods have been applied to the derivation of optimal therapies for this HIV infection [8,9,10,11,12,13,14]. All these methods are based on HIV models which ignore the intracellular delay by assuming that the infectious process is instantaneous; that is, as soon as the virus enters an uninfected cell, it starts to produce virus particles; this is not reasonable biologically.
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