Related papers: Stochastic epidemics in a homogeneous community
A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that…
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…
In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by…
This document is the Part IV of the book 'Stochastic Epidemic Models with Inference' edited by Tom Britton and Etienne Pardoux. It is written by Catherine Lar\'edo, with the contribution of Viet Chi Tran for the Chapter 4. Epidemic data…
We study an individual-based stochastic epidemic model in which infected individuals become susceptible again following each infection. In contrast to classical compartment models, after each infection, the infectivity is a random function…
In order to model an epidemic, different approaches can be adopted. Mainly, the deterministic approach and the stochastic one. Recently, a large amount of literature has been published using the two approaches. The aim of this paper is to…
Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated stochastic model, whose law of large numbers…
We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states…
We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…
An individual-based model of the infectious disease spread among the urban population is considered. A system of stochastic equations, which describes changes in quantities of four population groups, susceptible, exposed, infected…
During infectious disease epidemics, pathogen transmission occurs in host populations made up of interacting subpopulations. Using stochastic simulation and analytical approximations, we examine how outbreak sizes in networked populations…