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Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies

Purity Ngina, Rachel Waema Mbogo, Livingstone S. Luboobi
2018 Computational and Mathematical Methods in Medicine  
HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics.  ...  In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables.  ...  Acknowledgments The corresponding author acknowledges the financial support from the DAAD and the National Research Fund from the Kenyan Government.  ... 
doi:10.1155/2018/9385080 pmid:29971134 pmcid:PMC6008687 fatcat:bn32vgssojgnlo2w4sroc35pjm

Quantifying HTLV-I dynamics

Becca Asquith, Charles R M Bangham
2007 Immunology and Cell Biology  
Here, we review recent advances in mathematical modelling of HTLV-I infection and illustrate how mathematics has enabled us to identify factors that determine an individual's viral burden and risk of developing  ...  Despite significant advances in our understanding of the immune response to persistent viruses like human T-cell lymphotropic virus type I (HTLV-I), many important questions remain unanswered.  ...  The role of the CD8+ cytotoxic T lymphocyte (CTL) immune response in controlling HIV-1 infection is an active research area for many groups.  ... 
doi:10.1038/sj.icb.7100050 pmid:17372609 fatcat:5pvs6viqmvagjppgxzdl6ohxom

A comparison of computational efficiencies of stochastic algorithms in terms of two infection models

Kathryn Link, Kaitlyn Gayvert, Brandi Canter, Anna Broido, Michele Joyner, Shuhua Hu, H. Thomas Banks
2012 Mathematical Biosciences and Engineering  
To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within  ...  The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy.  ...  The term δ E E 1 T * 1 is used to account for the elimination of infected activated CD4+ T cells T * 1 by the HIV-specific effector CD8+ T cells (that is, T * 1 is eliminated from the system at rate δ  ... 
doi:10.3934/mbe.2012.9.487 pmid:22881023 fatcat:4ilvvaeuyzgc7di74ngsxr4z44

An Optimal Control Approach to HIV Immunology

Edilson F. Arruda, Claudia M. Dias, Camila V. de Magalhães, Dayse H. Pastore, Roberto C. A. Thomé, Hyun Mo Yang
2015 Applied Mathematics  
This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body.  ...  This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells.  ...  Acknowledgements The authors would like to thank FAPESP (Projeto temático Fapesp, 09/15098-0), and the Carlos Chagas Filho  ... 
doi:10.4236/am.2015.66102 fatcat:6v7fex5ta5hh5b2t3tu466km54

How Many Human Immunodeficiency Virus Type 1-Infected Target Cells Can a Cytotoxic T-Lymphocyte Kill?

W. D. Wick, O. O. Yang, L. Corey, S. G. Self
2005 Journal of Virology  
Here we employ mathematical models of the infection process and CTL action to estimate the rate that CTLs can kill HIV-1-infected cells from in vitro and in vivo data.  ...  The antiviral role of CD8 ؉ cytotoxic T lymphocytes (CTLs) in human immunodeficiency virus type 1 (HIV-1) infection is poorly understood.  ...  Greenberg for valuable discussions about the adoptive transfer experiments and B. Walker and S. Kalams for providing the CTL clones for the in vitro assays.  ... 
doi:10.1128/jvi.79.21.13579-13586.2005 pmid:16227278 pmcid:PMC1262579 fatcat:pay272clana6tevjsz7qyooobi

Mathematical Modeling Predicts that Increased HSV-2 Shedding in HIV-1 Infected Persons Is Due to Poor Immunologic Control in Ganglia and Genital Mucosa

Joshua T. Schiffer, David A. Swan, Amalia Magaret, Timothy W. Schacker, Anna Wald, Lawrence Corey, Scott N Mueller
2016 PLoS ONE  
Peak episode viral load was not found to differ between HIV infected and uninfected participants regardless of CD4+ T-cell count.  ...  While the general mechanism underlying this observation is deficient CD4+T-cell function, it is unknown whether increased severity of herpes virus infections is due primarily to poor immune control in  ...  The reproductive number is the average number of cells that an infected cell would infect assuming the presence of CD8+ T-cells.  ... 
doi:10.1371/journal.pone.0155124 pmid:27285483 pmcid:PMC4902308 fatcat:mth2ovqeqnaefcutukyyytxwhe

A fractional diffusion model of CD8+T cells response to parasitic infection in the brain

Afshin Farhadi, Emmanuel Hanert
2022 Mathematical Modelling of Natural Phenomena  
Furthermore, we derive a mathematical model representing CD8 + T cell response to infected brain cells.  ...  In the field of immunology, a large number of studies have shown that effector CD8 + T cells respond to T. gondii infection in the brain tissue through controlling the proliferation of intracellular parasites  ...  Mathematical models are useful tools to study how the search strategies performed by T cells can lead to an efficient immune response against pathogens.  ... 
doi:10.1051/mmnp/2022003 fatcat:wd4psjnwkjb5tdjyeamn2mfenu

Dynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review [article]

Miguel Ramos Pascual
2020 arXiv   pre-print
Cytokines and immunoglobulins specific for each antigen (i.e. gp41 or p24) have been also included in the model, modelling the atraction effect of CD4 T-cells to the infected area and the reduction of  ...  A dynamic model of non-lineal time-dependent ordinary differential equations (ODE) has been applied to the interactions of a HIV infection with the immune system cells.  ...  The model will be applied in the future also to simulate the effect of antiviral drugs against HIV infection, such as the HAART therapy.  ... 
arXiv:2008.02388v1 fatcat:j5s4wfgmgncibkwmk4o4r5vljm

Theoretical Design of a Gene Therapy To Prevent AIDS but Not Human Immunodeficiency Virus Type 1 Infection

L. S. Weinberger, D. V. Schaffer, A. P. Arkin
2003 Journal of Virology  
Since the crHIV-1 gene therapy model is a system of stiff differential equations, a Rosenbrock method was used to solve the system of equations.  ...  I T cells are also assumed to die at the same rate as T cells since the crHIV-1 is not produced in the absence of HIV-1 infection (an assumption that can be relaxed for some specific therapeutic payloads  ... 
doi:10.1128/jvi.77.18.10028-10036.2003 pmid:12941913 pmcid:PMC224590 fatcat:j3ezjeqy3bhftoljlkjnoyc5wm

Tensor based approach to the numerical treatment of the parameter estimation problems in mathematical immunology

Valeriya V. Zheltkova, Dmitry A. Zheltkov, Zvi Grossman, Gennady A. Bocharov, Eugene E. Tyrtyshnikov
2018 Journal of Inverse and Ill-Posed Problems  
In this study we consider a standard parameter estimation problem for two models, formulated as ODEs systems: the model of HIV infection and BrdU-labeled cell division model.  ...  The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization.  ...  We formulate a mathematical model of HIV infection by extending the Marchuk-Petrov model of an antiviral immune response.  ... 
doi:10.1515/jiip-2016-0083 fatcat:qmcubcwmrfc4jg6aooowbvpnke

Uncertainty quantification in modeling HIV viral mechanics

H. T. Banks, Robert Baraldi, Karissa Cross, Kevin Flores, Christina McChesney, Laura Poag, Emma Thorpe
2015 Mathematical Biosciences and Engineering  
We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7] .  ...  We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data.  ...  Acknowledgements 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  ... 
doi:10.3934/mbe.2015.12.937 pmid:26280189 fatcat:mr5nf4xtcfearbemyojxio4bdm

Modelling the Human Immune System by Combining Bioinformatics and Systems Biology Approaches

Nicolas Rapin, Can Kesmir, Sune Frankild, Morten Nielsen, Claus Lundegaard, Søren Brunak, Ole Lund
2006 Journal of biological physics (Print)  
In this paper, we outline a framework for integration of these two approaches. As an example, we develop a model in which HIV dynamics are correlated with genomics data.  ...  the virus in the mathematical model.  ...  Acknowledgements The authors wish to thank Rob de Boer for insightful and inspiring discussions about the mathematical model.  ... 
doi:10.1007/s10867-006-9019-7 pmid:19669470 pmcid:PMC2651529 fatcat:dhjfamtoofbrdhlyufwvrezs5y

Particle swarm optimization based estimation of HIV-1 viral load in resource limited settings

Kamalan K, Mannar Jawahar P
2013 African Journal of Microbiology Research  
The efficiency of the proposed method was evaluated using error analysis and correlation analysis. The average error in estimation of HIV-1 viral load was found to be 3.317%.  ...  Such countries depend on CD4 tests as an alternative. In this work, a method for estimating the HIV-1 viral load from CD4 cell counts, using Particle Swarm Optimization (PSO) technique was proposed.  ...  MATERIALS AND METHODS In this work, an attempt has been made to estimate the HIV-1 viral load from CD4 cell count in the acute and chronic phase of the HIV-1 infection.  ... 
doi:10.5897/ajmr12.1924 fatcat:a7v6sdodzjeb5hjgwu4mqf7f4y

Mathematical Modeling of Ultradeep Sequencing Data Reveals that Acute CD8+ T-Lymphocyte Responses Exert Strong Selective Pressure in Simian Immunodeficiency Virus-Infected Macaques but Still Fail To Clear Founder Epitope Sequences

T. M. T. Love, S. W. Thurston, M. C. Keefer, S. Dewhurst, H. Y. Lee
2010 Journal of Virology  
The prominent role of antiviral cytotoxic CD8 ؉ T-lymphocytes (CD8-TL) in containing the acute viremia of human and simian immunodeficiency viruses (HIV-1 and SIV) has rationalized the development of T-cell-based  ...  Our estimate of SIV acute escape rates was found to be comparable to very early HIV-1 escape rates.  ...  for the critical review of the manuscript.  ... 
doi:10.1128/jvi.00117-10 pmid:20335256 pmcid:PMC2876615 fatcat:llekw23s3fgbnbpunxny7nd3g4

Modeling the within-host dynamics of HIV infection

Alan S Perelson, Ruy M Ribeiro
2013 BMC Biology  
Here we review developments in HIV modeling, emphasizing quantitative findings about HIV biology uncovered by studying acute infection, the response to drug therapy and the rate of generation of HIV variants  ...  We show how modeling has revealed many dynamical features of HIV infection and how it may provide insight into the ultimate cure for this infection.  ...  In these models, the interactions between virus, CD4+ T cells and CD8+ T cells were considered [89] , as HIV-induced depletion of CD4+ T cells may affect one's ability to mount CD8+ T-cell responses  ... 
doi:10.1186/1741-7007-11-96 pmid:24020860 pmcid:PMC3765939 fatcat:ts6zsnfkanhdvextwfbhqauxpm
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