Related papers: A model for infection on graphs
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node…
We study the SIR epidemic model with infections carried by $k$ particles making independent random walks on a random regular graph. Here we assume $k\leq n^{\epsilon}$, where $n$ is the number of vertices in the random graph, and $\epsilon$…
To understand the contact patterns of a population -- who is in contact with whom, and when the contacts happen -- is crucial for modeling outbreaks of infectious disease. Traditional theoretical epidemiology assumes that any individual can…
In this article, we proposed a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that…
The transmission dynamics of some infectious diseases is related to the contact structure between individuals in a network. We used five algorithms to generate contact networks with different topological structure but with the same…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
We study competing first passage percolation on graphs generated by the configuration model with infinite-mean degrees. Initially, two uniformly chosen vertices are infected with type 1 and type 2 infection, respectively, and the infection…
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…
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 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…
Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so.…
We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this…
Researchers, policy makers, and engineers need to make sense of data on spreading processes as diverse as viral infections, water contamination, and misinformation in social networks. Classical questions include predicting infection…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
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…