Related papers: Critical case stochastic phylogenetic tree model v…
Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing…
This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully…
This study proposes a nonhomogeneous birth--death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth-death processes with $n$…
Consider a supercritical Crump--Mode--Jagers process such that all births are at integer times (the lattice case). We show that under a certain condition on the intensity of the offspring process, the second-order fluctuations of the age…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
In this article, we consider time-changed models of population evolution $\mathcal{X}^f(t)=\mathcal{X}(H^f(t))$, where $\mathcal{X}$ is a counting process and $H^f$ is a subordinator with Laplace exponent $f$. In the case $\mathcal{X}$ is a…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
An important problem in evolutionary genomics is to investigate whether a certain trait measured on each sample is associated with the sample phylogenetic tree. The phylogenetic tree represents the shared evolutionary history of the samples…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…
There is considerable theoretical and experimental support to the proposal that tissue homeostasis in the adult skin can be represented as a critical branching process. The homeostatic condition requires that the proliferation rate of the…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
For a birth-death process subject to catastrophes, defined on the state-space $S=\{r,r+1,r+2,...\}$, with $r$ a positive integer or zero, the first-visit time to a state $k\in S$ is considered and the Laplace transform of its probability…
A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years.…
Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular…
This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…