Modeling the immune response to HIV infection

Conway, Jessica M.; Ribeiro, Ruy M.

doi:10.1016/j.coisb.2018.10.006

Cited by 19 publications

(14 citation statements)

References 122 publications

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“…There is a tradition of mathematical models that consider populations of infectious agents, target cells and infected cells [24,25,[66][67][68][69][70]. The usual assumption that new infectious agents are produced at a rate proportional to the number of infected cells, perhaps after an "eclipse" phase [27,28], may be appropriate in situations where infected cells, independently, release new infectious agents, one or a few at a time, on multiple occasions during their lifetime, a process known as "budding" [32]. It is more problematic when infectious particles are released in a single "burst" as the infected cell dies.…”

Section: Discussionmentioning

confidence: 99%

“…In such models, the rate of production of new infected cells is assumed to be proportional to the number of infected cells, which is true if each infected cell, independently, releases infectious particles at a constant rate. It is possible to go beyond the simplest hypothesis by considering subpopulations of infected cells: in an "eclipse" phase or productive phase [27,28], or considering different multiplicities of infection and co-infection [29]. In this work, we seek to describe an scenario where bacteria continue to divide inside the host cell, without any being released from the cell, until the host cell ultimately ruptures, typically releasing more than a hundred bacteria at a time [23,[30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic dynamics of Francisella tularensis infection and replication

et al. 2020

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We study the pathogenesis of Francisella tularensis infection with an experimental mouse model, agent-based computation and mathematical analysis. Following inhalational exposure to Francisella tularensis SCHU S4, a small initial number of bacteria enter lung host cells and proliferate inside them, eventually destroying the host cell and releasing numerous copies that infect other cells. Our analysis of disease progression is based on a stochastic model of a population of infectious agents inside one host cell, extending the birth-anddeath process by the occurrence of catastrophes: cell rupture events that affect all bacteria in a cell simultaneously. Closed expressions are obtained for the survival function of an infected cell, the number of bacteria released as a function of time after infection, and the total bacterial load. We compare our mathematical analysis with the results of agent-based computation and, making use of approximate Bayesian statistical inference, with experimental measurements carried out after murine aerosol infection with the virulent SCHU S4 strain of the bacterium Francisella tularensis, that infects alveolar macrophages. The posterior distribution of the rate of replication of intracellular bacteria is consistent with the estimate that the time between rounds of bacterial division is less than 6 hours in vivo.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic dynamics of Francisella tularensis infection and replication

et al. 2020

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“…The myth that mathematical models made important conceptual contributions to basic and clinical immunology has been perpetuated in numerous reports and reviews, mostly in the biomathematical literature [e.g., (95)] but also in biological and general journals [e.g., (92, 96)]. In fact, to my knowledge no mathematical modeling-based studies in immunology at the cellular or systemic levels to date provided groundbreaking insights, or correct answers to key questions about causality.…”

Section: While Paradigms Evolved Mainstream Mathematical Modeling Hamentioning

confidence: 99%

Immunological Paradigms, Mechanisms, and Models: Conceptual Understanding Is a Prerequisite to Effective Modeling

Grossman

2019

Front. Immunol.

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Most mathematical models that describe the individual or collective actions of cells aim at creating faithful representations of limited sets of data in a self-consistent manner. Consistency with relevant physiological rules pertaining to the greater picture is rarely imposed. By themselves, such models have limited predictive or even explanatory value, contrary to standard claims. Here I try to show that a more critical examination of currently held paradigms is necessary and could potentially lead to models that pass the test of time. In considering the evolution of paradigms over the past decades I focus on the “smart surveillance” theory of how T cells can respond differentially, individually and collectively, to both self- and foreign antigens depending on various “contextual” parameters. The overall perspective is that physiological messages to cells are encoded not only in the biochemical connections of signaling molecules to the cellular machinery but also in the magnitude, kinetics, and in the time- and space-contingencies, of sets of stimuli. By rationalizing the feasibility of subthreshold interactions, the “dynamic tuning hypothesis,” a central component of the theory, set the ground for further theoretical and experimental explorations of dynamically regulated immune tolerance, homeostasis and diversity, and of the notion that lymphocytes participate in nonclassical physiological functions. Some of these efforts are reviewed. Another focus of this review is the concomitant regulation of immune activation and homeostasis through the operation of a feedback mechanism controlling the balance between renewal and differentiation of activated cells. Different perspectives on the nature and regulation of chronic immune activation in HIV infection have led to conflicting models of HIV pathogenesis—a major area of research for theoretical immunologists over almost three decades—and can have profound impact on ongoing HIV cure strategies. Altogether, this critical review is intended to constructively influence the outlook of prospective model builders and of interested immunologists on the state of the art and to encourage conceptual work.

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“…To date, only a few host-level models [ 4 , 5 ] have been developed to understand the SARS-CoV-2 replication cycle and its interactions with the immune system. Most of them are linked to HIV [ 14 ], hepatitis virus [ 15 ], Ebola [ 16 ], influenza [ 9 , 17 ], and other models.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a within-host model of SARS-CoV-2

Nath¹,

Dehingia

Mishra

et al. 2021

Adv Differ Equ

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In this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number $(\chi _{0})$ ( χ 0 ) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection.

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Modeling the immune response to HIV infection

Cited by 19 publications

References 122 publications

Stochastic dynamics of Francisella tularensis infection and replication

Stochastic dynamics of Francisella tularensis infection and replication

Immunological Paradigms, Mechanisms, and Models: Conceptual Understanding Is a Prerequisite to Effective Modeling

Mathematical analysis of a within-host model of SARS-CoV-2

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