Related papers: Near-critical SIR epidemic on a random graph with …
Stochastic infection processes are continuous-time Markov chains on graphs that assign each vertex one of multiple states, such as susceptible, infected, or recovered. Depending on the model, vertices change their state based on random…
We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s_c. Using percolation theory to calculate the average…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
The SIRS process is a continuous-time process for how infections spread on a graph. In this model, each vertex is in one of the following three states: susceptible (to the infection; S), infected (I), or recovered (R) and thus immune to the…
This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and Windridge (2014).
We consider the Susceptible-Infected-Recovered (SIR) epidemic model on a Euclidean network in one dimension in which nodes at a distance $l$ are connected with probability $P(l) \propto l^{-\delta}$ in addition to nearest neighbors. The…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that…
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and…
Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…
In this paper, we are concerned with SIR epidemics in a random environment on complete graphs, where every edges are assigned with i.i.d. weights. Our main results give large and moderate deviation principles of sample paths of this model.
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that,…
In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where…
Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved.…
In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and…
The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most $B$…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental…