Related papers: Bounding basic characteristics of spatial epidemic…
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability…
In this paper, we propose a Boltzmann-type kinetic model of the spreading of an infectious disease on a network. The latter describes the connections among countries, cities or districts depending on the spatial scale of interest. The…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role…
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…
In this work we investigate a bootstrap percolation process on random graphs generated by a random graph model which combines preferential attachment and edge insertion between previously existing vertices. The probabilities of adding…
We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a…
In this paper we consider a simple virus infection spread model on a finite population of $n$ agents connected by some neighborhood structure. Given a graph $G$ on $n$ vertices, we begin with some fixed number of initial infected vertices.…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…
We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin $S$ = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis…
We study a simple model of epidemics where an infected node transmits the infection to its neighbors independently with probability $p$. This is also known as the independent cascade or Susceptible-Infected-Recovered (SIR) model with fixed…
We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
Weight distribution largely impacts the epidemic spreading taking place on top of networks. This paper studies a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation…
In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the…
The current work deals with an epidemic model on the complete graph K_n on n vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types differ in the probability of getting infected, and/or in the…
The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for…
In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…