Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B

Marchuk, G. I.; Петров, Р. В.; Romanyukha, A. A.; Bocharov, Gennady

doi:10.1016/s0022-5193(05)80142-0

Cited by 68 publications

(58 citation statements)

References 54 publications

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“…5 is solved by y(t) = a u [ae-u(t-T) -ue-a(t-T)] [11] for t > T, the same functional expression as that of v(t) in a treatment with reverse transcriptase inhibitors (Eq. 10).…”

Section: Protease Inhibitors and Combined Drug Treatmentmentioning

confidence: 99%

See 1 more Smart Citation

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Herz

Bonhoeffer²,

Anderson³

et al. 1996

Proc. Natl. Acad. Sci. U.S.A.

399

285

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Anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.Clinical studies of drug therapy in patients infected with the human immunodeficiency virus type 1 (HIV-1) (1-4) or the hepatitis B virus (HBV) (5) provide for the possibility of estimating important kinetic constants of virus replication in vivo.In HIV-1 infection, treatment with reverse transcriptase or protease inhibitors results in a decline of free virus in several distinct phases (see Fig. 1). Initially, the plasma virus load remains at approximately pretreatment levels which are quasistationary on the time scale of weeks in the asymptomatic stage of the infection. This "shoulder" is followed by a rapid and approximately exponential decline of plasma virus and an increase in CD4 cell counts. The reduction of virus load is caused by two factors: decay of productively infected cells and clearance of free virus particles. Finally, the decline flattens out and virus levels may even rise again. This is a consequence of some combination of the following factors: (i) the drug not being 100% effective, (ii) reservoirs of long-lived cells that continuously produce virus particles, and (iii) the emergence of resistant virus (1,(6)(7)(8).If the clearance rate of free virus particles is significantly faster than the decay rate of productively infected cells, the slope of the exponential decline provides an estimate of the turnover rate of productively infected cells. Neglecting intracellular delays, the length and shape of the shoulder then reflect the turnover rate of free plasma virus (1, 4). Within this modeling ...

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“…5 is solved by y(t) = a u [ae-u(t-T) -ue-a(t-T)] [11] for t > T, the same functional expression as that of v(t) in a treatment with reverse transcriptase inhibitors (Eq. 10).…”

Section: Protease Inhibitors and Combined Drug Treatmentmentioning

confidence: 99%

“…Half-lives of productively infected cells seem to vary greatly among different patients, ranging from 10 to 100 days (5,11). Interestingly, plasma virus clearance in patients treated with reverse transcriptase inhibitors is seemingly achieved in the absence of any antibodies to free virus particles.…”

Section: Hepatitis B Dynamicsmentioning

confidence: 99%

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Herz

Bonhoeffer²,

Anderson³

et al. 1996

Proc. Natl. Acad. Sci. U.S.A.

399

285

View full text Add to dashboard Cite

show abstract

“…На активность NK-клеток оказывают влияние различные цитокины и гормоны, произ-водимые организмом. В данной работе учитыва-ется угнетающее влияние кортизола и стимули-рующее влияние интерлейкина-2 [24,28,36].…”

Section: создана математическая модель регуляции противовирусного иммunclassified

“…Состояние устойчивости временно, и далее клетка переходит в состояние рефрак-терности, невосприимчивости к воздействию интерферона на некоторое время [33]. Основ-ными механизмами специфического приобре-тенного иммунного ответа являются производ-ство В-клетками антител [16], связывающих свободные вирусы, и уничтожение зараженных вирусом клеток цитотоксическими T-лимфо-цитами [36]. Запуск активного деления выше-указанных клеток иммунного ответа происходит после первых сигналов организма о наличии ви-русной инфекции через стимулирующее влия-ние интерлейкина-2.…”

Section: создана математическая модель регуляции противовирусного иммunclassified

Mathematical Model for Describing Anti-Virus Immune Response Regulation Allowing for Functional Disorders in a Body

Trusov¹,

Zaitseva²,

Chigvintsev³

et al. 2017

Health Risk Analysis

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В настоящее время проблема описания взаимосвязи адаптивных систем, изменяющих свое функционирование с целью сохранения оптимального состояния при изменении внеш-них условий, представляет значительный инте-рес для исследователей как в области нейроэн-докринной регуляции, так и иммунных меха-низмов [25, 30]. В работах данного направления описываются различные проявления взаимных регуляторных влияний [17, 41]. В исследовани-ях показывается нейроэндокринная регуляция иммунной системы [4, 19, 29] и управляющее __________________________

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“…Antia and Koella, 1994;Antia et al, 1996;Nowak and Bangham, 1996;Kleinstein and Seiden, 2000;Pugliese and Gandolfi, 2008) and models that focus on a particular (mostly human) disease of interest (e.g. Marchuck et al, 1991;Wodarz, 2003;Kosmrlj et al, 2010;Smith and Ribeiro, 2010). Models differ widely in the level of detail and the temporal and spatial scales at which immune processes are represented as well as in their methodologies.…”

Section: Prrsv (Virus) Infection (See Example 1)mentioning

confidence: 99%

The role of mathematical models of host–pathogen interactions for livestock health and production – a review

Doeschl‐Wilson

2011

Animal

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Compared with the application of mathematical models to study human diseases, models that describe animal responses to pathogen challenges are relatively rare. The aim of this review is to explain and show the role of mathematical host-pathogen interaction models in providing underpinning knowledge for improving animal health and sustaining livestock production. Existing host-pathogen interaction models can be assigned to one of three categories: (i) models of the infection and immune system dynamics, (ii) models that describe the impact of pathogen challenge on health, survival and production and (iii) models that consider the co-evolution of host and pathogen. State-of-the-art approaches are presented and discussed for models belonging to the first two categories only, as they concentrate on the host-pathogen dynamics within individuals. Models of the third category fall more into the class of epidemiological models, which deserve a review by themselves. An extensive review of published models reveals a rich spectrum of methodologies and approaches adopted in different modelling studies, and a strong discrepancy between models concerning diseases in animals and models aimed at tackling diseases in humans (most of which belong to the first category), with the latter being generally more sophisticated. The importance of accounting for the impact of infection not only on health but also on production poses a considerable challenge to the study of host-pathogen interactions in livestock. This has led to relatively simplistic representations of host-pathogen interaction in existing models for livestock diseases. Although these have proven appropriate for investigating hypotheses concerning the relationships between health and production traits, they do not provide predictions of an animal's response to pathogen challenge of sufficient accuracy that would be required for the design of appropriate disease control strategies. A synthesis between the modelling methodologies adopted in categories 1 and 2 would therefore be desirable. The progress achieved in mathematical modelling to study immunological processes relevant to human diseases, together with the current advances in the generation and analysis of biological data related to animal diseases, offers a great opportunity to develop a new generation of host-pathogen interaction models that take on a fundamental role in the study and control of disease in livestock.

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Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B

Cited by 68 publications

References 54 publications

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Mathematical Model for Describing Anti-Virus Immune Response Regulation Allowing for Functional Disorders in a Body

The role of mathematical models of host–pathogen interactions for livestock health and production – a review

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