Branching Processes with Biological Applications

We consider two new models of reducible age-dependent branching processes with emigration in conjunction with estimation problems arising in cell biology. Methods of statistical inference are developed using the relevant embedded discrete branching structure. Based on observations of the branching process with emigration, estimators of the offspring probabilities are proposed for the hidden unobservable process without emigration, which is of prime interest to investigators. The problem under consideration is motivated by experimental data generated by time-lapse video recording of cultured cells, which provides abundant information on their individual evolutions and thus on the basic parameters of their life cycle in tissue culture. Some parameters, such as the mean and variance of the mitotic cycle time, can be estimated nonparametrically without resorting to any mathematical model of cell population kinetics. For other parameters, such as the offspring distribution, a model-based inference is needed. A...

https://www.jstor.org/stable/info/27640188

Branching Processes as Models of Progenitor Cell Populations and Estimation of the Offspring Distributions

The erythroid lineage is a particularly sensitive target of radiation injury We model the dynamics of immature (BFU-E) and mature (CFU-E) erythroid progenitors, which have markedly different kinetics of recovery, following sublethal total body irradiation using a two-type reducible age-dependent branching process with immigration Properties of the expectation and variance of the frequencies of both types of progenitors are presented Their explicit expressions are derived when the process is Markovian, and their asymptotic behavior is identified in the age-dependent (non-Markovian) case Analysis of experimental data on the kinetics of BFU-E and CFU-E reveals that the probability of self-renewal increases transiently for both cell types following sublethal irradiation In addition, the probability of self-renewal increased more for CFU-E than for BFU-E The strategy adopted by the erythroid lineage ensures replenishment of the BFU-E compartment while optimizing the rate of CFU-E recovery Finally, our analysis also indicates that radiation exposure causes a delay in BFU-E recovery consistent with injury to the hematopoietic stem/progenitor cell compartment that give rise to BFU-E Erythroid progenitor self-renewal is thus an integral component of the recovery of the erythron in response to stress

Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration.

Generalized superstatistics, i.e., a "statistics of superstatistics," is proposed. A generalized superstatistical system comprises a set of superstatistical subsystems and represents a generalized hyperensemble. There exists a random control parameter that determines both the density of energy states and the distribution of the intensive parameter for each superstatistical subsystem, thereby forming the third, upper level of dynamics. Generalized superstatistics can be used for nonstationary nonequilibrium systems. The system in which a supercritical multitype age-dependent branching process takes place is an example of a nonstationary generalized superstatistical system. The theory is applied to pair production in a neutron star magnetosphere.

Generalization of the Beck-Cohen superstatistics

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.

/pdf/stochastic-monotonicity-and-continuity-properties-of-the-2h472miozh.pdf

Stochastic monotonicity and continuity properties of the extinction time of bellman-harris branching processes: an application to epidemic modelling

Age and residual lifetime distributions for branching processes

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Age and residual lifetime distributions for branching processes