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

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Optimal Control ◽  
Immune Response ◽  
Hiv Infection ◽  
Equation Model ◽  
Difference Approximation ◽  
Infection Model ◽  
Optimal Controls ◽  
Control Pair ◽  
Hiv Infection Model ◽  
Delay Differential

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.

scholarly journals Delay Differential Model for Tumour-Immune Response with Chemoimmunotherapy and Optimal Control

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
F. A. Rihan ◽  
D. H. Abdelrahman ◽  
F. Al-Maskari ◽  
F. Ibrahim ◽  
M. A. Abdeen
Keyword(s):  
Optimal Control ◽  
Immune Response ◽  
Treatment Strategies ◽  
Tumour Cells ◽  
Optimal Controls ◽  
Control Pair ◽  
Differential Model ◽  
Effector Cells ◽  
Days Of Therapy ◽  
Delay Differential

We present a delay differential model with optimal control that describes the interactions of the tumour cells and immune response cells with external therapy. The intracellular delay is incorporated into the model to justify the time required to stimulate the effector cells. The optimal control variables are incorporated to identify the best treatment strategy with minimum side effects by blocking the production of new tumour cells and keeping the number of normal cells above 75% of its carrying capacity. Existence of the optimal control pair and optimality system are established. Pontryagin’s maximum principle is applicable to characterize the optimal controls. The model displays a tumour-free steady state and up to three coexisting steady states. The numerical results show that the optimal treatment strategies reduce the tumour cells load and increase the effector cells after a few days of therapy. The performance of combination therapy protocol of immunochemotherapy is better than the standard protocol of chemotherapy alone.

Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays

2014 ◽  
Vol 07 (05) ◽  
pp. 1450055 ◽  
Author(s):  
A. M. Elaiw ◽  
R. M. Abukwaik ◽  
E. O. Alzahrani
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Cell Mediated Immunity ◽  
Globally Asymptotically Stable ◽  
Global Properties ◽  
Hiv Infection Model ◽  
Ctl Immune Response

In this paper, we study the global properties of a human immunodeficiency virus (HIV) infection model with cytotoxic T lymphocytes (CTL) immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R0 and the immune response activation number [Formula: see text]. We have proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if [Formula: see text], then the infected steady state without CTL immune response is GAS, and if [Formula: see text], then the infected steady state with CTL immune response is GAS.

scholarly journals Analysis of an HIV infection model with treatments and delayed immune response

2016 ◽  
Vol 40 (4) ◽  
pp. 3081-3089 ◽  
Author(s):  
Dongwei Huang ◽  
Xiao Zhang ◽  
Yongfeng Guo ◽  
Hongli Wang
Keyword(s):  
Immune Response ◽  
Hiv Infection ◽  
Infection Model ◽  
Hiv Infection Model

scholarly journals A new optimal control technique for solution of HIV infection model

2021 ◽  
Vol 40 ◽  
pp. 1-7
Author(s):  
Malihe Najafi ◽  
Hadi Basirzadeh
Keyword(s):  
Optimal Control ◽  
Power Series ◽  
Hiv Infection ◽  
Numerical Solutions ◽  
Control Technique ◽  
Infection Model ◽  
Control Power ◽  
Hiv Infection Model ◽  
Power Series Technique ◽  
Series Technique

In this paper, by means of the optimal control technique and power series technique,we introduce a new method, namely, the optimal control power series technique, bywhich one can obtain numerical solutions of the HIV infection model of CD4+T cells.The obtained approximate solution has shown good agreement with the experimentalresults and previous simulations using other methods.https://search.hthereadinghub.com/?uc=20180302&ad=appfocus1&source=d-lp0-bb9&uid=0d8983d2-5a26-4ec4-bba5-84ea234d1896&i_id=ebooks_100.7&page=newtab&

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