Optimal control of an age-structured model of HIV infection

Abstract The optimal treatment strategies with an age-structured model of HIV infection are investigated. The age-structured model allows for variations in the virion production rate and the death rate of infected T cells as a function of age, which is the length of time since infection. The optimal therapy protocol is derived by formulating and analyzing an optimal control problem and the existence of solutions to the optimal control problem is established. The optimal treatment strategy is obtained by solving the corresponding optimality system numerically. It is demonstrated by numerical simulations that the dynamic treatment strategy delays the time to reach the peak viral load and reduces the viral load. Moreover, we propose that optimal therapy protocols should be changed according to different viral production rates and death rates of infected T cells.

[1]  Philip Laird,et al.  Dynamic Optimization , 1992, ML.

[2]  Helen Moore,et al.  A mathematical model for treatment-resistant mutations of hiv. , 2005, Mathematical biosciences and engineering : MBE.

[3]  M. Nowak,et al.  Specific therapy regimes could lead to long-term immunological control of HIV. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Angela R. McLean,et al.  Zidovudine and HIV: Mathematical models of within‐host population dynamics , 1995 .

[5]  Guanrong Chen,et al.  Feedback control of a biodynamical model of HIV-1 , 2001, IEEE Transactions on Biomedical Engineering.

[6]  J. Janssen,et al.  Deterministic and Stochastic Optimal Control , 2013 .

[7]  Chung Choo Chung,et al.  Optimal Scheduling of Drug Treatment for HIV Infection : Continuous Dose Control and Receding Horizon Control , 2003 .

[8]  Daniel Coombs,et al.  An age-structured model of hiv infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. , 2004, Mathematical biosciences and engineering : MBE.

[9]  Structured treatment interruption. , 2000, The AIDS reader.

[10]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[11]  D. Kirschner,et al.  Predicting differential responses to structured treatment interruptions during HAART , 2004, Bulletin of mathematical biology.

[12]  D. Kirschner,et al.  Optimal control of the chemotherapy of HIV , 1997, Journal of mathematical biology.

[13]  G. Webb.  Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[14]  A. N,et al.  Dynamic Multidrug Therapies for HIV : A Control Theoretic Approach , 1997 .

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

[16]  A S Perelson,et al.  Modeling plasma virus concentration during primary HIV infection. , 2000, Journal of theoretical biology.

[17]  G. M. Ortiz,et al.  Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection , 2000, AIDS.

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  M. Araki,et al.  Two-Degree-of-Freedom PID Controllers , 2003 .

[20]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[21]  J. Corbeil,et al.  Nevirapine resistance mutations of human immunodeficiency virus type 1 selected during therapy , 1994, Journal of virology.

[22]  D. Ho,et al.  The HIV-1 Vaccine Race , 2002, Cell.

[23]  Julianna Lisziewicz,et al.  Structured treatment interruptions in HIV/AIDS therapy. , 2002, Microbes and infection.

[24]  C. Boucher,et al.  Anti-CD4 therapy for AIDS suggested by mathematical models , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[26]  E. Blum,et al.  The Mathematical Theory of Optimal Processes. , 1963 .

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

[28]  Max Gunzburger,et al.  Perspectives in flow control and optimization , 1987 .

[29]  S. Lenhart,et al.  OPTIMIZING CHEMOTHERAPY IN AN HIV MODEL , 1998 .

[30]  José Álvarez-Ramírez,et al.  Feedback Control of the chemotherapy of HIV , 2000, Int. J. Bifurc. Chaos.

[31]  R. Paredes,et al.  Structured treatment interruption in chronically HIV-1 infected patients after long-term viral suppression , 2000, AIDS.

[32]  A two-strain hiv-1 mathematical model to assess the effects of chemotherapy on disease parameters. , 2005, Mathematical biosciences and engineering : MBE.