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Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing…
The contact process with an asymptomatic state, introduced in [Belhadji, Lanchier and Mercer, Stochastic Process. Appl., 176:104417, 2024], is a natural variant of the basic contact process that distinguishes between asymptomatic (state 1)…
We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a now classic approach, the first stage of the invasion is…
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…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge…
Mathematical models represent one of the fundamental ways of studying nature. In special, epidemic models have shown to be particularly useful in the understanding of the course of diseases and in the planning effective control policies. A…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $\varphi$ of the…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
We develop a class of exponential-family point processes based on a latent social space to model the coevolution of social structure and behavior over time. Temporal dynamics are modeled as a discrete Markov process specified through…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on…