BISTABILITY ANALYSIS OF AN HIV MODEL WITH IMMUNE RESPONSE

Some HIV-infected patients (the so-called post-treatment controllers) can control the virus after cessation of antiretroviral therapy. A small fraction of patients can even naturally maintain undetectable viral load without therapy (they are called elite controllers). The immune response may play an important role in viral control in these patients. In this paper, we analyze a within-host model including immune response to study the virus dynamics in HIV-infected patients. We derived two threshold values for the immune cell proliferation parameter. Below the lower immune proliferation rate, the model has a stable immune-free steady state, which predicts that patients have a high viral load. Above the higher immune proliferation rate, the model has a stable low infected steady state, which indicates that patients are under elite control. Between the two immune thresholds, the model exhibits the dynamic behavior of bistability, which suggests that patients either undergo viral rebound after treatment termin...

[1]  Yanni Xiao,et al.  Piecewise virus-immune dynamic model with HIV-1 RNA-guided therapy. , 2015, Journal of theoretical biology.

[2]  Jessica M Conway,et al.  Post-treatment control of HIV infection , 2015, Proceedings of the National Academy of Sciences.

[3]  Shigui Ruan,et al.  Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. , 2015, Mathematical biosciences and engineering : MBE.

[4]  Fucheng Liao,et al.  Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment , 2014 .

[5]  D. Richman,et al.  Absence of detectable HIV-1 viremia after treatment cessation in an infant. , 2013, The New England journal of medicine.

[6]  P. Kaleebu,et al.  Duration of HIV-1 Viral Suppression on Cessation of Antiretroviral Therapy in Primary Infection Correlates with Time on Therapy , 2013, PloS one.

[7]  Brigitte Autran,et al.  Post-Treatment HIV-1 Controllers with a Long-Term Virological Remission after the Interruption of Early Initiated Antiretroviral Therapy ANRS VISCONTI Study , 2013, PLoS pathogens.

[8]  Sanyi Tang,et al.  Predicting the HIV/AIDS epidemic and measuring the effect of mobility in mainland China. , 2013, Journal of theoretical biology.

[9]  C. Rouzioux,et al.  Hiv-1 Control after Transient Antiretroviral Treatment Initiated in Primary Infection: Role of Patient Characteristics and Effect of Therapy , 2012, Antiviral therapy.

[10]  Xinyu Song,et al.  Dynamics analysis of a delayed viral infection model with immune impairment , 2011 .

[11]  Gang Huang,et al.  Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response , 2011, Appl. Math. Lett..

[12]  D. Unutmaz,et al.  Revisiting Immune Exhaustion During HIV Infection , 2011, Current HIV/AIDS reports.

[13]  Xinyu Song,et al.  Stability and Hopf bifurcation for a viral infection model with delayed non-lytic immune response , 2010 .

[14]  Xinyu Song,et al.  A delayed HIV-1 infection model with Beddington–DeAngelis functional response , 2010 .

[15]  J. Blankson,et al.  Elucidating the elite: mechanisms of control in HIV-1 infection. , 2009, Trends in pharmacological sciences.

[16]  Gang Huang,et al.  Global properties for virus dynamics model with Beddington-DeAngelis functional response , 2009, Appl. Math. Lett..

[17]  Y. Takeuchi,et al.  Immune impairment in HIV infection: existence of risky and immunodeficiency thresholds. , 2009, Journal of theoretical biology.

[18]  Alan S. Perelson,et al.  Modeling Latently Infected Cell Activation: Viral and Latent Reservoir Persistence, and Viral Blips in HIV-infected Patients on Potent Therapy , 2009, PLoS Comput. Biol..

[19]  Libin Rong,et al.  Modeling HIV persistence, the latent reservoir, and viral blips. , 2009, Journal of theoretical biology.

[20]  Libin Rong,et al.  Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection. , 2009, Journal of theoretical biology.

[21]  Y. Takeuchi,et al.  Immune impairment thresholds in HIV infection. , 2009, Immunology letters.

[22]  D. Kirschner,et al.  A methodology for performing global uncertainty and sensitivity analysis in systems biology. , 2008, Journal of theoretical biology.

[23]  Alberto Gandolfi,et al.  A simple model of pathogen-immune dynamics including specific and non-specific immunity. , 2008, Mathematical biosciences.

[24]  Christian L. Althaus,et al.  Dynamics of Immune Escape during HIV/SIV Infection , 2008, PLoS Comput. Biol..

[25]  Xianning Liu,et al.  A chronic viral infection model with immune impairment. , 2007, Journal of theoretical biology.

[26]  Xianning Liu,et al.  Complex dynamic behavior in a viral model with delayed immune response , 2007 .

[27]  Alan S. Perelson,et al.  Viral and Latent Reservoir Persistence in HIV-1–Infected Patients on Therapy , 2006, PLoS Comput. Biol..

[28]  Dominik Wodarz,et al.  Boosting immunity by antiviral drug therapy: A simple relationship among timing, efficacy, and success , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Patrick W Nelson,et al.  Mathematical analysis of delay differential equation models of HIV-1 infection. , 2002, Mathematical biosciences.

[30]  Dominik Wodarz,et al.  The importance of lytic and nonlytic immune responses in viral infections. , 2002, Trends in immunology.

[31]  D. Wodarz,et al.  Persistent Virus Infection despite Chronic Cytotoxic T-Lymphocyte Activation in Gamma Interferon-Deficient Mice Infected with Lymphocytic Choriomeningitis Virus , 2000, Journal of Virology.

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

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

[34]  M A Nowak,et al.  Virus dynamics: the effect of target cell limitation and immune responses on virus evolution. , 1998, Journal of theoretical biology.

[35]  A S Perelson,et al.  Target cell limited and immune control models of HIV infection: a comparison. , 1998, Journal of theoretical biology.

[36]  Hadi Dowlatabadi,et al.  Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example , 1994 .

[37]  Horst R. Thieme,et al.  Persistence under relaxed point-dissipativity (with application to an endemic model) , 1993 .

[38]  Donald L. DeAngelis,et al.  A Model for Tropic Interaction , 1975 .

[39]  J. Beddington,et al.  Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency , 1975 .

[40]  J. P. Lasalle.  Some Extensions of Liapunov's Second Method , 1960 .

[41]  J. Blankson.  Effector mechanisms in HIV-1 infected elite controllers: highly active immune responses? , 2010, Antiviral research.

[42]  Libin Rong,et al.  Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips. , 2009, Mathematical biosciences.

[43]  Hal L. Smith,et al.  Virus Dynamics: A Global Analysis , 2003, SIAM J. Appl. Math..