A branching stochastic evolutionary model of the B-cell repertoire.

We propose a stochastic framework to describe the evolution of the B-cell repertoire during germinal center (GC) reactions. Our model is formulated as a multitype age-dependent branching process with time-varying immigration. The immigration process captures the mechanism by which founder B cells initiate clones by gradually seeding GC over time, while the branching process describes the temporal evolution of the composition of these clones.

Statistical modelling of COVID-19 pandemic development applying branching processes.

In this paper, a statistical model for COVID-19 infection dynamics is described, using only the observed daily statistics of infected individuals. For this purpose, two special classes of branching processes without or with an immigration component are considered. These models are intended to estimate the main parameter of the infection and to give a prediction of the mean value of the non-observed population of the infected individuals.

Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration.

We consider a class of Sevastyanov branching processes with non-homogeneous Poisson immigration. These processes relax the assumption required by the Bellman-Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations.

A test of homogeneity for age-dependent branching processes with immigration.

We propose a novel procedure to test whether the immigration process of a discretely observed age-dependent branching process with immigration is time-homogeneous. The construction of the test is motivated by the behavior of the coefficient of variation of the population size. When immigration is time-homogeneous, we find that this coefficient converges to a constant, whereas when immigration is time-inhomogeneous we find that it is time-dependent, at least transiently.

Asymptotic behavior of cell populations described by two-type reducible age-dependent branching processes with non-homogeneous immigration().

Stem and precursor cells play a critical role in tissue development, maintenance, and repair throughout the life. Often, experimental limitations prevent direct observation of the stem cell compartment, thereby posing substantial challenges to the analysis of such cellular systems. Two-type age-dependent branching processes with immigration are proposed to model populations of progenitor cells and their differentiated progenies.

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Populations.

Two-type reducible age-dependent branching processes with inhomogeneous immigration are considered to describe the kinetics of renewing cell populations. This class of processes can be used to model the generation of oligodendrocytes in the central nervous system or the kinetics of leukemia cells. The asymptotic behavior of the first and second moments, including the correlation, of the process is investigated.

Two-Type Reducible Age-Dependent Branching Processes With Non-Homogeneous Poisson Immigration.

Two type reducible age-dependent branching stochastic processes with non-homogeneous Poisson immigration are considered as models of renewal cell population dynamics. The asymptotic behaviour of the first moments of the process with or without immigration is investigated. Several classes of asymptotic behavior are identified for the population dynamics.

Limiting Distributions for Multitype Branching Processes.

In this paper the asymptotic behavior of multitype Markov branching processes with discrete or continuous time is investigated in the positive regular and nonsingular case when both the initial number of ancestors and the time tend to infinity. Some limiting distributions are obtained as well as multivariate asymptotic normality is proved. The paper considers also the relative frequencies of distinct types of individuals which is motivated by applications in the field of cell biology.

Modeling Cell Kinetics using Branching Processes with Non-Homogeneous Poisson Immigration.

Age-dependent branching processes with non-homogeneous Poisson immigration are proposed as models of cell proliferation kinetics. The asymptotic behaviour of the first and second-order moments is investigated and the obtained results are use to develop a relevant statistical inference.