Related papers: Individual based SIS models on (not so) dense larg…
We develop a framework for non-Markovian, well-mixed SIR and SIS models beyond mean field, utilizing the continuous-time random walk formalism. Using a gamma distribution for the infection and recovery inter-event times as a test case, we…
This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the…
Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analysing and controlling an epidemic outbreak. For some contact networks, it is possible to group…
We study an individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity. Each individual is associated with a random infection-age dependent…
We study how the spread of computer viruses, worms, and other self-replicating malware is affected by the logical topology of the network over which they propagate. We consider a model in which each host can be in one of 3 possible states -…
Consider an SI process on a graph $G$ where each S--I connection becomes I--I at rate $\lambda$. Here S and I stand for ``susceptible'' and ``infected'' respectively. The evoSI model is a modification of the SI model in which S--I edges are…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
The Susceptible-Infected-Susceptible (SIS) model is one of the simplest memoryless system for describing information/epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched…
Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the collective…
This paper deals with the spread of diseases over both a population network and an infrastructure network. We develop a layered networked spread model for a susceptible-infected-susceptible (SIS) pathogen-borne disease spreading over a…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
Recent work by Erik Volz [arXiv:0705.2092] has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to…
We present a novel approach to the study of epidemics on networks as thermodynamic phenomena, considering the thermodynamic efficiency of contagions, considered as distributed computational processes. Modelling SIS dynamics on a contact…
This paper considers the classical Susceptible--Infected--Susceptible (SIS) network epidemic model, which describes a disease spreading through $n$ nodes, with the network links governing the possible transmission pathways of the disease…
We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the \emph{Independent Cascade} process and the \emph{Reed-Frost} process in such graphs. These are…
Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in…
The identification of which nodes are optimal seeds for spreading processes on a network is a non-trivial problem that has attracted much interest recently. While activity has mostly focused on non-recurrent type of dynamics, here we…
In this paper, we derive nonasymptotic theoretical bounds for the influence in random graphs that depend on the spectral radius of a particular matrix, called the Hazard matrix. We also show that these results are generic and valid for a…
Pruning at Initialisation methods discover sparse, trainable subnetworks before training, but their theoretical mechanisms remain elusive. Existing analyses are often limited to finite-width statistics, lacking a rigorous characterisation…
A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…