Related papers: Stochastic domination for a hidden Markov chain wi…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
We present numerical results obtained from the modelling of a stochastic, highly connected and mobile community. The spread of attributes like health, disease among the community members is simulated using cellular automata on a planar 2…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
A class of stochastic vector-borne infectious disease models is derived and studied. The class type is determined by a general nonlinear incidence rate of the disease. The disease spreads in a highly random environment with variability from…
We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet…
This study aims to estimate the parameters of a stochastic exposed-infected epidemiological model for the transmission dynamics of notifiable infectious diseases, based on observations related to isolated cases counts only. We use the…