Related papers: The Stochastic Firefighter Problem
Forecasting disease spread is a critical tool to help public health officials design and plan public health interventions. However, the expected future state of an epidemic is not necessarily well defined as disease spread is inherently…
We consider the problem of identifying the source of an epidemic, spreading through a network, from a complete observation of the infected nodes in a snapshot of the network. Previous work on the problem has often employed geometric,…
Given a graph $G=(V,E)$, the problem of \gb{} is to find a sequence of nodes from $V$, called burning sequence, in order to burn the whole graph. This is a discrete-step process, in each step an unburned vertex is selected as an agent to…
The problem of firebreak placement is crucial for fire prevention, and its effectiveness at landscape scale will depend on their ability to impede the progress of future wildfires. To provide an adequate response, it is therefore necessary…
We study the problem of containing spreading processes in arbitrary directed networks by distributing protection resources throughout the nodes of the network. We consider two types of protection resources are available: (i) Preventive…
Finding influential spreaders of information and disease in networks is an important theoretical problem, and one of considerable recent interest. It has been almost exclusively formulated as a node-ranking problem -- methods for…
We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and derive the expected value of the infection process. Then as an…
We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…
The burning number $b(G)$ of a graph $G$ is the minimum number of rounds required to burn all vertices when, at each discrete step, existing fires spread to neighboring vertices and one new fire may be ignited at an unburned vertex. This…
We study epidemic spreading processes in large networks, when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\`a-vis the underlying network…
Network-based epidemic models have been extensively employed to understand the spread of infectious diseases, but have generally overlooked the fact that most realistic networks are dynamical rather than static. In this paper, we study a…
The spread of an infection on a real-world social network is determined by the interplay of two processes: the dynamics of the network, whose structure changes over time according to the encounters between individuals, and the dynamics on…
In this paper we propose a method for sparse dynamic allocation of resources to bound the risk of spreading processes, such as epidemics and wildfires, using convex optimization and dynamic programming techniques. Here, risk is defined as…
We consider the spread of a supercritical stochastic SIR (Susceptible, Infectious, Recovered) epidemic on a configuration model random graph. We mainly focus on the final stages of a large outbreak and provide limit results for the duration…
We consider the problem of finding the graph on which an epidemic cascade spreads, given only the times when each node gets infected. While this is a problem of importance in several contexts -- offline and online social networks,…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
We consider a SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of…
The way diseases spread through schools, epidemics through countries, and viruses through the Internet is crucial in determining their risk. Although each of these threats has its own characteristics, its underlying network determines the…
Graph burning is one model for the spread of memes and contagion in social networks. The corresponding graph parameter is the burning number of a graph $G$, written $b(G)$, which measures the speed of the social contagion. While it is…
An epidemic spreading in a network calls for a decision on the part of the network members: They should decide whether to protect themselves or not. Their decision depends on the trade-off between their perceived risk of being infected and…