Related papers: How old is this bird? The age distribution under s…
We consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…
This book handles the fatty liver disease from the bio-statistical point of view . It discusses the disease process in the simple general form of health-disease-death multi-states model . Continuous Time Markov Chains are used to estimate…
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of…
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
Progressive diseases worsen over time and are characterised by monotonic change in features that track disease progression. Here we connect ideas from two formerly separate methodologies -- event-based and hidden Markov modelling -- to…
Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
We study out of equilibrium dynamics and aging for a particle diffusing in one dimensional environments, such as the random force Sinai model, as a toy model for low dimensional systems. We study fluctuations of two times $(t_w, t)$…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…
Cell populations invade through a combination of proliferation and motility. Proliferation depends on the internal timing of cell division: how long cells take to complete the cell cycle. This timing varies substantially within (and across)…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
In this paper, we introduce and study an age-structured epidemiological compartment model and its respective problem, applied but not limited to the COVID-19 pandemic, in order to investigate the role of the age of the individuals in the…
We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…
We introduce a nonparametric bootstrap procedure based on a dynamic factor model to construct pointwise prediction intervals for period life-table death counts. The age distribution of death counts is an example of constrained data, which…
We examine the age-structured SIR model, a variant of the classical Susceptible-Infected-Recovered (SIR) model of epidemic propagation, in the context of COVID-19. In doing so, we provide a theoretical basis for the model, perform an…
In this paper we propose a multi-state model for the evaluation of the conversion option contract. The multi-state model is based on age-indexed semi-Markov chains that are able to reproduce many important aspects that influence the…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
Aging is considered as the property of the elements of a system to be less prone to change states as they get older. We incorporate aging into the noisy voter model, a stochastic model in which the agents modify their binary state by means…