Related papers: Birth/birth-death processes and their computable t…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements -…
Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle…
A method yielding simple relationships among bilateral birth-and-death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first-passage-time densities…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability…
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…
We consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ from odd states. We determine the probability generating functions of the even…
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described.…
We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classical birth-death process introduced by Feller (1939). We…
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…
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…
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…
We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…
In this paper, we use a linear birth and death process with immigration to model infectious disease propagation when contamination stems from both person-to-person contact and contact with the environment. Our aim is to estimate the…
Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…
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…
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…
The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach.…
We study two time-changed variants of the birth-death process with catastrophe where the time-changing components are the first hitting times of the stable subordinator and the tempered stable subordinator. For both the processes, we derive…