Optimal Control of a Delayed HIV Infection Model via Fourier Series

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.

Optimal Control of a Time Delayed HIV-1 Infection Model

“…Garira et al [4] used two controls strategies which simulate the effect of reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) to integrate drug efficacy. Ghanbari and Farahi [5] obtained optimal control pair for nonlinear delay HIV model with quadratic cost functional by using Fourier series approximation. Recent research work has been focused on optimal control problem of delayed HIV model (see for example [7,8,10,11] ).…”