Modeling HIV Immune Response and Validation with Clinical Data

Abstract

A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain important features that have been shown important by recent experimental research are incorporated in the model. These include the role of CD4+ memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. The phenomenon of "viral blips" experienced by some patients on therapy with viral load levels suppressed below the detection limit is also investigated. Censored clinical data is used to demonstrate that this model provides reasonable fits to all the patient data available for this study and, moreover, that it exhibits impressive predictive capability. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

“…The model describes two co-circulating populations of target cells, potentially representing CD4 + T-lymphocytes (S 1 ) and macrophages (S 2 ) (or perhaps activated and resting CD4 + T cells; see Banks et al 2008). We refer the reader to Adams et al (2004Adams et al ( , 2005, for an explanation of the source and death rates for these cell populations and focus our discussion on the interactions particularly relevant to drug treatment and STI scenarios.…”

“…We consider the optimal strategies for effecting a transfer between these steady states in the minimum duration of treatment periods. Recently, the model and an improved model including a compartment for CD4 + memory cells have been validated with clinical data and have been shown to possess significant predictive capabilities with data at the individual patient level (Adams et al 2007;Banks et al 2008). The models in these reports have multiple locally asymptotically stable off-treatment equilibria.…”

Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions

“…In this scenario, a subset of infected cells harbor the virus in a latent state in which the virus is not produced at all or at undetected levels [6], [7]. Since ART targets the various stages of viral replication, HIV-1 that is integrated into the DNA of reservoir cells can evade ART and reseed the HIV-1 infection when patients are taken off ART [1], [8].…”

“…Among HIV-1 patients This research was supported in part by grant number NIAID R01AI071915-10 from the National Institute of Allergy and Infectious Diseases, in part by the National Science Foundation by Undergraduate Biomathematics grant number DBI-1129214 and in part by the National Science Foundation under grant number DMS-0946431. 1 Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC, USA *Corresponding author, htbanks@ncsu.edu that require ART, those treated during the earliest stages of infection have a smaller reservoir than those treated at later stages [11]. Furthermore, some patients that are able to suppress HIV-1 after the termination of long-term ART therapy have low HIV-1 reservoirs in central-memory CD4 T cells [2].…”

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We consider a model for in-host HIV-1 infection dynamics developed and validated with patient data in earlier work [1]. We revisit the earlier model in light of progress over the last several years in understanding of HIV-1 progression in humans.

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