Linear Clustering Process on Networks

We propose a linear clustering process on a network consisting of two opposite forces: attraction and repulsion between adjacent nodes. Each node is mapped to a position on a one-dimensional line. The attraction and repulsion forces move the nodal position on the line, depending on how similar or different the neighbourhoods of two adjacent...

Time-dependent solution of the NIMFA equations around the epidemic threshold

The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible...

The Viral State Dynamics of the Discrete-Time NIMFA Epidemic Model

The majority of research on epidemics relies on models which are formulated in continuous-time. However, processing real-world epidemic data and simulating epidemics is done digitally and the continuous-time epidemic models are usually approximated by discrete-time models. In general, there is no guarantee that properties of continuous-time...

Exact Network Reconstruction from Complete SIS Nodal State Infection Information Seems Infeasible

The SIS dynamics of the spread of a virus crucially depend on both the network topology and the spreading parameters. Since neither the topology nor the spreading parameters are known for the majority of applications, they have to be inferred from observations of the viral spread. We propose an inference method for both topology and spreading...

Network localization is unalterable by infections in bursts

To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a...