Branching stochastic processes with immigration in analysis of renewing cell populations

Yakovlev, Andrei; Yanev, Nikolai

doi:10.1016/j.mbs.2006.06.001

Cited by 36 publications

(29 citation statements)

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“…Moreover, from a practical outlook, it has been used to describe the evolution of populations over time in different situations, including, for example, to solve many problems related to cell populations (see, for example, [4], [5], [12], [17], [19], [26], and [27]). …”

Section: Introductionmentioning

confidence: 99%

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

2010

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The aim of this paper is to study the stochastic monotonicity and continuity properties of the extinction time of Bellman-Harris branching processes depending on their reproduction laws. Moreover, we show their applications in an epidemiological context, obtaining an optimal criterion to establish the proportion of susceptible individuals in a given population that must be vaccinated in order to eliminate an infectious disease. First the spread of infection is modelled by a Bellman-Harris branching process. Finally, we provide a simulation-based method to determine the optimal vaccination policies.

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Section: Introductionmentioning

confidence: 99%

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

2010

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“…Branching models have been applied to many biological problems in such fields as epidemiology, genetics, and cell dynamics. Examples include the evolution of infectious diseases (e.g., Mode and Sleemam (2000), Ball et al (2004), or Garske and Rhodes (2008)), population genetics (e.g., Campbell (2003) or Iwasa et al (2005)), and stem cells (e.g., Yakovlev and Yanev (2006)). Further examples are reviewed in the recent monographs of Kimmel and Axelrod (2002) and Pakes (2003), and in the communication of Caron-Lormier et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Bisexual branching processes to model extinction conditions for Y-linked genes

González

Martínez

Mota

2009

Journal of Theoretical Biology

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In a two-sex monogamic population, the evolution of the number of carriers of the two alleles of a Y-linked gene is considered. To this end, a multitype bisexual branching model is presented in which it is assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit constitute the key to determining the extinction or survival of each allele. Moreover, the destiny of each allele in the population is found not to depend on the behaviour of the other.

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“…One good example is oligodendricyte population dynamics that motivated the models introduced by Boucher et al [39] [40]. There, as in the general Yakovlev-Yanev framework [41] that also includes immigration, the usual branching hypotheses are adopted. For oligodendricytes, using time-lapse photography to follow sibling cells, these hypotheses were checked by Hyrien et al [42].…”

Section: Discussionmentioning

confidence: 99%

On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics

Duffy

Subramanian

2008

J. Math. Biol.

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During an adaptive immune response, lymphocytes proliferate for five to twenty five cell divisions, then stop and die over a period of weeks. Based on extensive flow cytometry data, Hawkins et al. (PNAS, 2007, 104, 5032-5037) introduced a cell-level stochastic model of lymphocyte population dynamics, called the Cyton Model, that accurately captures mean lymphocyte population size as a function of time. In Subramanian et al. (J. Math. Biol., 2008, 56:6, 861-892), we performed a branching process analysis of the Cyton Model and deduced from parameterizations for in vitro and in vivo data that the immune response is predictable despite each cell's fate being highly variable.One drawback of flow cytometry data is that individual cells cannot be tracked, so that it is not possible to investigate dependencies in the fate of cells within family trees. In the absence of this information, while the Cyton Model abandons one of the usual assumptions of branching processes (the independence of lifetime and progeny number), it adopts another of the standard branching processes hypotheses: that the fates of progeny are stochastically independent. However, new experimental observations of lymphocytes show that the fates of cells in the same family tree are not stochastically independent. Hawkins et al. (2008, submitted for publication) report on ciné lapse photography experiments where every founding cell's family tree is recorded for a system of proliferating lymphocytes responding to a mitogenic stimulus. Data from these experiments demonstrate that the death-ordivision fates of collaterally consanguineous cells (those in the same generation within a founding cell's family tree) are strongly correlated, while there is little correlation between cells of distinct generations and between cells in distinct family trees.As this finding contrasts with one of the assumptions of the Cyton Model, in this paper we introduce three variants of the Cyton Model with increasing levels of collaterally consanguineous correlation Ken Duffy and Vijay Subramanian, Hamilton Institute, National University of Ireland, Maynooth, Ireland E-mail: {ken.duffy, vijay.subramanian}@nuim.ie 2 structure to incorporate these new found dependencies. We investigate their impact on the predicted expected variability of cell population size. Mathematically we conclude that while the introduction of correlation structure leaves the mean population size unchanged from the Cyton Model, the variance of the population size distribution is typically larger. Biologically, through comparison of model predictions for Cyton Model parameterizations determined by in vitro and in vivo experiments, we deduce that if collaterally consanguineous correlation extends beyond cousins, then the immune response is less predictable than would be concluded from the original Cyton Model. That is, some of the variability seen in data that we previously attributed to experimental error could be due to intrinsic variability in the cell population size dynamics.

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Branching stochastic processes with immigration in analysis of renewing cell populations

Cited by 36 publications

References 50 publications

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

Bisexual branching processes to model extinction conditions for Y-linked genes

On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics

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