Related papers: On the basic reproduction number in continuously s…
We consider a model of stationary population with random size given by a continuous state branching process with immigration with a quadratic branching mechanism. We give an exact elementary simulation procedure of the genealogical tree of…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
The effective reproduction number $R_t$ measures an infectious disease's transmissibility as the number of secondary infections in one reproduction time in a population having both susceptible and non-susceptible hosts. Current approaches…
This work simulates the developmental process of cortical neurogenesis, initiating from a single stem cell and governed by gene regulatory rules derived from mouse single-cell transcriptomic data. The developmental process spontaneously…
The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts…
Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…
Some populations, such as red blood cells (RBCs), exhibit a pattern of population decline that is closer to linear rather than exponential, which has proven to be unexpectedly challenging to describe with a single simple mathematical model.…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals…
We show that the generation time -- a notion usually described in a biological context -- can be defined in a general way as a return time in a conveniently constructed finite Markov chain. The simple formula we obtain agrees with previous…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate…
Maintenance of sexual reproduction and genetic recombination imposes physiological costs when compared to parthenogenic reproduction, most prominently: for maintaining the corresponding (molecular) machinery, for finding a mating partner,…
The aim of this paper is to understand the extreme variability on the estimated reproduction ratio $R_0$ observed in practice. For expository purpose we consider a discrete time stochastic version of the Susceptible-Infected-Recovered (SIR)…
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects…
Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
It is known that the majority of the human genome consists of repeated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from repeated sequences and has mutated to its current form. In…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…