Related papers: A note on monotonicity of spatial epidemic models
We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
The spreading of an epidemic is determined by the connectiviy patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erd\H{o}s-R\'{e}nyi random graph but, during the course of the epidemic,…
We consider a Spatial Markov Chain model for the spread of viruses. The model is based on the principle to represent a graph connecting nodes, which represent humans. The vertices between the nodes represent relations between humans. In…
We study a generalization of the classical contact process (SIS epidemic model) in a directed graph $G$. Our model is a continuous-time interacting particle system in which at every time, each vertex is either healthy or infected, and each…
The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of…
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…
Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with a small number of individuals, and because…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate…
We study equilibrium distancing during epidemics. Distancing reduces the individual's probability of getting infected but comes at a cost. It creates a single-peaked epidemic, flattens the curve and decreases the size of the epidemic. We…
The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian…
The spread of disease through a physical-contact network and the spread of information about the disease on a communication network are two intimately related dynamical processes. We investigate the asymmetrical interplay between the two…
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur…
Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
We consider rooted subgraphs in random graphs, i.e., extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three connecting two given vertices. In 1989, Spencer gave sufficient…