Related papers: The Stochastic Firefighter Problem
An infection spreads in a binary tree of height n as follows: initially, each leaf is either infected by one of k states or it is not infected at all. The infection state of each leaf is independently distributed according to a probability…
Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel…
Vaccination and outbreak monitoring are essential tools for preventing and minimizing outbreaks of infectious diseases. Targeted strategies, where the individuals most important for monitoring or preventing outbreaks are selected for…
In this paper, a susceptible-infected-susceptible (SIS) model with identical infectivity, where each node is assigned with the same capability of active contacts, $A$, at each time step, is presented. We found that on scale-free networks,…
Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network…
We introduce an immunization method where the percentage of required vaccinations for immunity are close to the optimal value of a targeted immunization scheme of highest degree nodes. Our strategy retains the advantage of being purely…
We consider a distribution network for delivering a natural resource or physical good to a set of nodes, each of which serves a set of customers, in which disruptions may occur at one or more nodes. Each node receives flow through a path…
We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible…
Graph burning is a discrete-time process that models the propagation of information in a network. Initially, we have an undirected graph of unburned vertices. At each time step, an unburned vertex is chosen to burn; additionally, unburned…
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,…
The success of an infectious disease to invade a population is strongly controlled by the population's specific connectivity structure. Here a network model is presented as an aid in understanding the role of social behavior and…
During infectious disease epidemics, pathogen transmission occurs in host populations made up of interacting subpopulations. Using stochastic simulation and analytical approximations, we examine how outbreak sizes in networked populations…
Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that…
Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in…
Given a social network represented by a graph $G$, we consider the problem of finding a bounded cardinality set of nodes $S$ with the property that the influence spreading from $S$ in $G$ is as large as possible. The dynamics that govern…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
We study the problem of parameter estimation based on infection data from an epidemic outbreak on a graph. We assume that successive infections occur via contagion; i.e., transmissions can only spread across existing directed edges in the…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
We consider the problem of distributing a vaccine for immunizing a scale-free network against a given virus or worm. We introduce a new method, based on vaccine dissemination, that seems to reflect more accurately what is expected to occur…
We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many…