Related papers: A multitype Galton-Watson model for rejuvenating c…
We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with…
Conditioning a multitype Galton-Watson process to stay alive into the indefinite future leads to what is known as its associated $Q$-process. We show that the same holds true if the process is conditioned to reach a positive threshold or a…
We consider a multi-type Galton-Watson branching processes, where the largest in magnitude positive eigenvalue $\rho$ of the first moments matrix is close to unity. Specifically, we examine the random vector representing the number of…
We study the iterated Galton-Watson process (IGW), possibly with thinning, introduced by Gawe{\l}and Kimmel to model the number of repeats of DNA triplets during some genetic disorders. If the process involves some thinning, then extinction…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
A stochastic genetic model for biological aging is introduced bridging the gap between the bit-string Penna model and the Pletcher-Neuhauser approach. The phenomenon of exponentially increasing mortality function at intermediate ages and…
We consider a generational and continuous-time two-phase model of the cell cycle. The first model is given by a stochastic operator, and the second by a piecewise deterministic Markov process. In the second case we also introduce a…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
In this paper we consider a generalization to the asexual version of the Penna model for biological aging, where we take a continuous time limit. The genotype associated to each individual is an interval of real numbers over which Dirac…
This paper proposes an original theory of aging of multicellular organisms. The cells of multicellular organisms, in contrast to unicellular organisms, are burdened with a two- part genome: housekeeping and specialized (multicellular),…
We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
We take up the challenge of designing realistic computational models of large interacting cell populations. The goal is essentially to bring Gillespie's celebrated stochastic methodology to the level of an interacting population of cells.…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
The stochastic simulation algorithm commonly known as Gillespie's algorithm is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular…
We introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The growth rate,…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…