Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method

Abstract

We present a delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4 + T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin's maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm based on the forward and backward difference approximation.

Modeling of a delay induced biochemical system for product optimization

“…Hence, equation (27) has no positive roots. Thus, equation (26) has no positive roots as F R (0) = α 3 > 0.…”

Quantitative Approximability of Optimal Control by Linear Programing Model for Asymptomatic Dual HIV - Pathogen Infections

“…Cytotoxic lymphocytes are often subdivided into precursors (CTLp) and effectors (CTLe). Other considered state components includes: critical role of time-delay immunity period (or delay intracellular) and the functioning capacities of therapeutic chemotherapies, which are generally classified into two families of HAART -reverse transcriptase inhibitors (RTI) and protease inhibitors (PIs) [11][12][13][14][15][16]. In most recent dimensions, indepth evaluations of viral load have resulted to the inclusion of viral aggressiveness index denoted as r state  variable.…”

Quantum Optimal Control Dynamics for Delay Intracellular and Multiple Chemotherapy Treatment (MCT) of Dual Delayed HIV - Pathogen Infections

“…The amiable quest of tackling this life threatening disease -HIV/AIDS infection has been through the application of mathematical modeling, which allows the utilization of significant knowledge of numerical methods for the optimization of host target immune system cells and the minimization of systemic cost, while suppressing viral victors below detectable clinical assay, see for examples the studies of models [1][2][3][4].…”

“…Articulating the above seeming silent but unavoidable epidemiological constraints and motivated by the studies [1,5], the present paper proposes and formulates using ordinary differential equations, an improved complex nonlinear 10-Dimensional dual HIV-pathogen dynamic delay-differential model, prime with the task of not only overcoming the lapses of model [16] but also to account for the methodological application of multiple chemotherapy treatment (MCT) in dual delay HIV-pathogen infections incorporated with delay intracellular and immune effectors response. Therefore, the present model is studied under the auspices of 10-subpopulations, which includes the critical roles of immune effectors response and two treatment functions 1 () t  and 2 () t …”

“…Furthermore, to appreciate the critical functions of delay intracellular immune andeffectors response, we leap on the innovative ideas of the mathematical formulations studied by [1,5]. Thus, in the quantitative analysis of our complex nonlinear model to be presented as on optimal control problemand applying from the vast branches of numerical methods, we explore Hamilton-Pontryagin' function to establish the model quantum locally optimal algorithm for successive approximations.…”