相关论文: The Contact Process on a Graph Adapting to the Inf…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
The contact process is a simple model for the spread of an infection in a structured population. We consider a variant of this process on Bienaym\'e-Galton-Watson trees, where vertices are equipped with a random fitness representing…
We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of the…
We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…
People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper…
We study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…
We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the integers that is assumed to be invariant under index shifts…
The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate $\lambda$ and infected individuals recover ($1 \longrightarrow 0$)…
We study the contact process on the complete graph on $n$ vertices where the rate at which the infection travels along the edge connecting vertices $i$ and $j$ is equal to $ \lambda w_i w_j / n$ for some $\lambda >0$, where $w_i$ are i.i.d.…
We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability…
We show that the contact process on a random $d$-regular graph initiated by a single infected vertex obeys the "cutoff phenomenon" in its supercritical phase. In particular, we prove that when the infection rate is larger than the critical…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…
We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message passing approach to temporal networks. The shift in perspective from node- to edge-centric quantities enables accurate modelling…
This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…
We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate $1$ and…
We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end we…
Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with…
Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…