Related papers: A generating function approach to Markov chains un…
We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by…
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,…
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…
Mast fruiting represents a synchronous population behaviour which can spread on large landscape areas. This reproductive pattern is generally perceived as a synchronous periodic production of large seed crops and has a significant practical…
We introduce a model to study the impact of catastrophes on evolutionary paths. If we do not allow catastrophes the number of changes in the maximum fitness of a population grows logarithmically with respect to time. Allowing catastrophes…
We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…
Multivariate Krawtchouk polynomials are constructed explicitly as Birth and Death polynomials, which have the nearest neighbour interactions. They form the complete set of eigenpolynomials of a birth and death process with the birth and…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
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 introduce a continuous-time Markov chain framework for estimating population size from multi-list data, which allows directional interactions to be modelled and can accommodate absorbing lists, such as death records, or more general data…
The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
Dynamical systems with components whose sizes evolve according to multiplicative stochastic rules have been recently combined with entry and exit processes. We show that the assumptions usually made in modeling exits are at odds with the…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
A $M/M/1$ queue with catastrophes is a modified $M/M/1$ queue model for which, according to the times of a Poisson process, catastrophes occur leaving the system empty. In this work, we study a fractional $M/M/1$ queue with catastrophes,…
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…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…