相关论文: A model for an epidemic with contact tracing and c…
We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate…
The correct identification of clusters is crucial for an accurate monitoring of the spread of a disease and also in many other natural, social and physical phenomena which exhibit an epidemic structure. Nevertheless, even when an accurate…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
We consider a class of Crump-Mode-Jagers processes with interaction, constructed by removing a newly born offspring with a probability that depends on the age structure of the population at its birth time. We prove a law of large numbers…
Clusters of infected individuals are defined on data from health laboratories, but this quantity has not been defined and characterized by epidemy models on statistical physics. For a system of mobile agents we simulate a model of infection…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical…
We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement of control measures. We show that the…
Quarantining and contact tracing are popular ad hoc practices for mitigating epidemic outbreaks. However, few mathematical theories are currently available to asses the role of a network in the effectiveness of these practices. In this…
We consider a stochastic epidemic model with sideward contact tracing. We assume that infection is driven by interactions within mixing events (gatherings of two or more individuals). Once an infective is diagnosed, each individual who was…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump-Mode-Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new…
We prove a Central Limit Theorem for the proportion of infected individuals for an epidemic model by dealing with a discrete time system of simple random walks on a complete graph with n vertices. Each random walk makes a role of a virus.…
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…
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…
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…
We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random lengths. This random graph representation is used to characterise the fractions of individuals infected by the different types of…
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
We investigate the effects of heterogeneous and clustered contact patterns on the timescale and final size of infectious disease epidemics. The abundance of transitive relationships (the number of 3 cliques) in a network and the variance of…