Related papers: Individual based SIS models on (not so) dense larg…
It has been shown in the past that many real-world networks exhibit community structures and non-trivial clustering which comes with the occurrence of a notable number of triangular connections. Yet the influence of such connection patterns…
Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring…
The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamics on random networks having a power law degree distribution with exponent $\gamma>3$ has been investigated using different mean-field approaches, which predict…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
Single virus epidemics over complete networks are widely explored in the literature as the fraction of infected nodes is, under appropriate microscopic modeling of the virus infection, a Markov process. With non-complete networks, this…
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 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…
There are many methods to estimate the quasi-stationary infected fraction of the SIS process on (random) graphs. A challenge is to adequately incorporate correlations, which is especially important in sparse graphs. Methods typically are…
The outbreak of a pandemic, such as COVID-19, causes major health crises worldwide. Typical measures to contain the rapid spread usually include effective vaccination and strict interventions (Nature Human Behaviour, 2021). Motivated by…
One model of real-life spreading processes is First Passage Percolation (also called SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with i.i.d.~heavy-tailed passage times on edges.…
We study the Susceptible-Infected-Recovered (SIR) and the Susceptible-Exposed-Infected-Recovered (SEIR) models of epidemics, with possibly time-varying rates, on a class of networks that are locally tree-like, which includes sparse…
Can graph neural networks generalize to graphs that are different from the graphs they were trained on, e.g., in size? In this work, we study this question from a theoretical perspective. While recent work established such transferability…
In this paper we investigate a susceptible-infected-susceptible (SIS) epidemic model describing data dissemination in opportunistic networks with heterogeneous setting of transmission parameters. We obtained the estimation of the final…
This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee the fast extinction of epidemic spread in a susceptible-infected-susceptible (SIS) model. We consider a Markov…
Network epidemics is a ubiquitous model that can represent different phenomena and finds applications in various domains. Among its various characteristics, a fundamental question concerns the time when an epidemic stops propagating. We…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…
We study the spread of an SIRS-type epidemic with vaccination on network. Starting from an exact Markov description of the model, we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends…