Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling

Bocharov, Gennady; Chereshnev, V. А.; Гайнова, И.А.; Bazhan, Sergei I.; Bachmetyev, B.A.; Argilaguet, Jordi; Martinez, Javier P; Meyerhans, Andreas

doi:10.1051/mmnp/20127507

Cited by 38 publications

(44 citation statements)

References 268 publications

(195 reference statements)

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“…An important direction in mathematical modeling in immunology is the development of mathematical models of the dynamics of HIV-1 infection in the human lymphatic system [1,2]. Mostly, these models are divided into deterministic and stochastic one.…”

Section: Introductionmentioning

confidence: 99%

Stochastic compartmental model of HIV-1 infection

Loginov

Pertsev

2020

ITM Web Conf.

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Stochastic model of the dynamics of HIV-1 infection describing the interaction of target cells and viral particles in the lymphatic nodes and their movement between the lymphatic nodes is constructed. The lymphatic system is represented as a graph, vertices of which are the lymphatic nodes and edges are the lymphatic vessels. The novelty of the model consists in the description of populations of cells and viral particles in terms of a multidimensional birth and death process with the random point-distributions. The random pointdistributions describe the duration of the transition of cells and viral particles between the lymph nodes and the duration of the stages of their development. The durations of transitions of viral particles and cells between the lymphatic nodes are not random and based on the rate of lymph flow. The durations of the developmental stages of infected target cells are assume to be constant. The graph theory for the formalization and compact representation of the model is used. An algorithm for modelling the dynamics of the studied populations is constructed basing on the Monte-Carlo method. The results of computational experiments for a system consisting of five lymphatic nodes are presented. *

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Section: Introductionmentioning

confidence: 99%

Stochastic compartmental model of HIV-1 infection

Loginov

Pertsev

2020

ITM Web Conf.

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“…Some of the model parameters can be assessed from other published mathematical models [4,5,19,29,42]. However, there is a subset of parameters that are unique to this model and additional data are required in order for these parameters to be quantified.…”

Section: Parameter Estimation For the Hiv Modelmentioning

confidence: 99%

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

Zheltkova

Zheltkov

Grossman

et al. 2017

Journal of Inverse and Ill-Posed Problems

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Abstract:The development of efficient computational tools for data assimilation and analysis using multiparameter models is one of the major issues in systems immunology. The mathematical description of the immune processes across different scales calls for the development of multiscale models characterized by a high dimensionality of the state space and a large number of parameters. 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 data fitting is formulated as global optimization of variants of least squares objective function. A new computational method based on Tensor Train (TT) decomposition is applied to solve the formulated problem. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. The method demonstrated a better performance in comparison with some other broadly used global optimization techniques.

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“…HIV infection inspired an extensive research involving mathematical modeling. The paper by Bocharov et al [7] reviews the fundamental biology and current concepts of HIV infection pathogenesis and the mathematical models proposed for studying HIV infection dynamics. A remarkable potential of the human immunodeficiency virus to change via mutation, multi-infection and recombination processes limits the ability of the immune system to control the infection as well as the efficiency of the antiviral treatments.…”

Section: Mathematics Subject Classification: 92-02 92-06mentioning

confidence: 99%

Preface. Distributed Parameter Systems in Immunology

Banks

Bocharov

Grossman

et al. 2012

Math. Model. Nat. Phenom.

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Mathematical modelling in immunology is about forty years old. This is a great age implying a symphony of experience, creativity and energy. Ever since, there is an increasing attempt to utilize the inherent precision of mathematics to enhance the analytical tools of basic and applied research in immunology. Despite numerous publications on application of mathematical models in immunology, the major communities of the experimental scientists and mathematicians are still disconnected. The genuine integration of modeling and simulation into the immunological mainstream remains a challenge.The immune system represents a complex and tightly regulated set of physical, biochemical and immunological processes occurring in time and space, the outcome of which is dependent on a large number of intra-and inter-cellular parameters. Coordinating a functional immune response requires tightly regulated communication between the cells of the immune system, which occurs in the form of cell-to-cell contact and the release of soluble factors that bind cognate receptors expressed by the cells. The functioning of the immune system involves feedback regulated spatially distributed proliferation,

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Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling

Cited by 38 publications

References 268 publications

Stochastic compartmental model of HIV-1 infection

Stochastic compartmental model of HIV-1 infection

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

Preface. Distributed Parameter Systems in Immunology

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