On the design of human immunodeficiency virus treatment based on a non-linear time-delay model.

Mathematical modelling and methods from control theory can be employed to find appropriate drug regimens in human immunodeficiency virus (HIV) treatment. In this study, using a non-linear time-delay model, the authors design some suboptimal highly active antiretroviral therapy (HAART) [http://www.en.wikipedia.org/wiki/Protease_inhibitor_%28pharmacology%29] regimens for patients with HIV. The non-linear delayed model is used to describe the dynamical interactions between HIV and human immune system in the presence of HAART. Based on the model, a set point tracking problem is defined in order to set the number of susceptible CD4+T cells to a desired value. To solve this set point tracking problem in a suboptimal way, the authors introduce a new method which is able to consider constraints on the amount of drug dosage. It is proved that the proposed method is able to set the number of susceptible CD4+T cells to the desired value. Simulation results confirm that the method is efficient even in the presence of parametric uncertainties.

[1]  D. Ian Wilson,et al.  Planning of patient-specific drug-specific optimal HIV treatment strategies , 2009 .

[2]  Thomas Hillen,et al.  A mathematical model for M-phase specific chemotherapy including the G0-phase and immunoresponse. , 2007, Mathematical biosciences and engineering : MBE.

[3]  Gareth Witten,et al.  Stability analysis of a model for HIV infection with RTI and three intracellular delays , 2009, Biosyst..

[4]  Hem Raj Joshi,et al.  Optimal control of an HIV immunology model , 2002 .

[5]  F. D. Souza.  Modeling the dynamics of HIV-1 and CD4 and CD8 lymphocytes , 1999 .

[6]  H. Maurer,et al.  Optimal control problems with delays in state and control variables subject to mixed control–state constraints , 2009 .

[7]  Y. Batmani,et al.  Optimal chemotherapy in cancer treatment: state dependent Riccati equation control and extended Kalman filter , 2013 .

[8]  Etsujiro Shimemura,et al.  The linear-quadratic optimal control approach to feedback control design for systems with delay , 1988, Autom..

[9]  C. Li,et al.  Optimal tracking control for large-scale interconnected systems with time-delays , 2007, Comput. Math. Appl..

[10]  Alberto d'Onofrio,et al.  Delay-induced oscillatory dynamics of tumour-immune system interaction , 2010, Math. Comput. Model..

[11]  S. Ruan,et al.  A delay-differential equation model of HIV infection of CD4(+) T-cells. , 2000, Mathematical biosciences.

[12]  A. Perelson.  Modelling viral and immune system dynamics , 2002, Nature Reviews Immunology.

[13]  Gabriele Pannocchia,et al.  A Model Predictive Control Strategy Toward Optimal Structured Treatment Interruptions in Anti-HIV Therapy , 2010, IEEE Transactions on Biomedical Engineering.

[14]  Tayfun Çimen,et al.  Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis , 2012 .

[15]  H. Banks,et al.  Optimal control of linear time-delay systems , 1969 .

[16]  Huan Qi,et al.  Qualitative analysis of hepatitis B virus infection model with impulsive vaccination and time delay , 2011 .

[17]  Xiangdong Liu,et al.  Analysis of the dynamics of a delayed HIV pathogenesis model , 2010, J. Comput. Appl. Math..

[18]  Carla M. A. Pinto,et al.  Mathematical model for HIV dynamics in HIV-specific helper cells , 2014, Commun. Nonlinear Sci. Numer. Simul..

[19]  Peeyush Chandra,et al.  Modeling the dynamics of HIV and CD4+ T cells during primary infection , 2010 .

[20]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[21]  B. Adams,et al.  Dynamic multidrug therapies for hiv: optimal and sti control approaches. , 2004, Mathematical biosciences and engineering : MBE.

[22]  Xinyu Song,et al.  Properties of stability and Hopf bifurcation for a HIV infection model with time delay , 2010 .

[23]  B. Adams,et al.  HIV dynamics: Modeling, data analysis, and optimal treatment protocols , 2005 .

[24]  Hamid Khaloozadeh,et al.  Open- and Closed-Loop Multiobjective Optimal Strategies for HIV Therapy Using NSGA-II , 2011, IEEE Transactions on Biomedical Engineering.

[25]  D. Greenhalgh,et al.  Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model , 2013 .

[26]  Patrizio Colaneri,et al.  Optimal therapy scheduling for a simplified HIV infection model , 2013, Autom..

[27]  Harvey Thomas Banks,et al.  A state‐dependent Riccati equation‐based estimator approach for HIV feedback control , 2006 .

[28]  Hee-Dae Kwon,et al.  Optimal treatment strategies derived from a HIV model with drug-resistant mutants , 2007, Appl. Math. Comput..

[29]  Defang Liu,et al.  A novel time delayed HIV/AIDS model with vaccination & antiretroviral therapy and its stability analysis , 2013 .

[30]  James D. Johnson,et al.  MATHEMATICAL MODELS OF SUBCUTANEOUS INJECTION OF INSULIN ANALOGUES: A MINI-REVIEW. , 2009, Discrete and continuous dynamical systems. Series B.

[31]  Tayfun Çimen,et al.  Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method , 2010, Annu. Rev. Control..

[32]  Shengqiang Liu,et al.  A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data. , 2012, Mathematical biosciences.