Conditional propagation of chaos in a spatial stochastic epidemic model with common noise

  title={Conditional propagation of chaos in a spatial stochastic epidemic model with common noise},
  author={Yen V. Vuong and Maxime Hauray and {\'E}tienne Pardoux},
  journal={Stochastics and Partial Differential Equations: Analysis and Computations},
We study a stochastic spatial epidemic model where the N individuals carry two features: a position and an infection state, interact and move in $${\mathbb {R}}^d$$ R d . In this Markovian model, the evolution of infection states are described with the help of the Poisson Point Processes , whereas the displacement of individuals are driven by mean field interactions, a (state dependence) diffusion and also a common noise, so that the spatial dynamic is a random process. We prove that when the… 

Propagation of chaos for a stochastic particle system modelling epidemics

We consider a simple stochastic N -particle system, already studied by the same authors in Ciallella et al (2021b), representing different populations of agents. Each agent has a label describing his



A spatial stochastic epidemic model: law of large numbers and central limit theorem

We consider an individual-based SIR stochastic epidemic model in continuous space. The evolution of the epidemic involves the rates of infection and cure of individuals. We assume that individuals

Conditional propagation of chaos for mean field systems of interacting neurons

We study the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and L\"ocherbach (2016) in a diffusive scaling. The system consists of $N$ neurons, each

Quantitative Propagation of Chaos in a Bimolecular Chemical Reaction-Diffusion Model

It is proved that in the large particle limit the stochastic dynamics converges to a mean field limit which is described by a nonlocal reaction-diffusion partial differential equation.

The scaling laws of human travel

It is shown that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two-parameter continuous-time random walk model to a surprising accuracy, and concluded that human travel on geographical scales is an ambivalent and effectively superdiffusive process.

Propagation of chaos for interacting particles subject to environmental noise.

A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are

Propagation of chaos for the Landau equation with moderately soft potentials

We consider the 3D Landau equation for moderately soft potentials ($\gamma\in(-2,0)$ with the usual notation) as well as a stochastic system of $N$ particles approximating it. We first establish some

A parsimonious model for spatial transmission and heterogeneity in the COVID-19 propagation

The framework developed here, in particular the non-local model and the associated estimation procedure, is of general interest in studying spatial dynamics of epidemics and has the ability to accurately track the COVID-19 epidemic curves.

A parsimonious approach for spatial transmission and heterogeneity in the COVID-19 propagation

Raw data on the number of deaths at a country level generally indicate a spatially variable distribution of COVID-19 incidence. An important issue is whether this pattern is a consequence of

Some epidemic systems are long range interacting particle systems

We present some recent results about dynamical interacting particle systems in the setting of epidemiology. The individuals are particles whose states (of health) depend on their relative positions.

The universal visitation law of human mobility.

A simple and robust scaling law is revealed that captures the temporal and spatial spectrum of population movement on the basis of large-scale mobility data from diverse cities around the globe and gives rise to prominent spatial clusters with an area distribution that follows Zipf's law.