Related papers: Explicit solutions of the Bass and SI models on hy…
Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H. The exact value of this quantity is known only for…
Modeling the spread of infections on networks is a well-studied and important field of research. Most infection and diffusion models require a real value or probability on the edges of the network as an input, but this is rarely available…
Spreading (diffusion) of innovations is a stochastic process on social networks. When the key driving mechanism is peer effects (word of mouth), the rate at which the aggregate adoption level increases with time depends strongly on the…
An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does…
In this paper we study a susceptible infectious recovered (SIR) model with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of differential equations for…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
We introduce a method to prove metastability of the contact process on Erd\H{o}s-R\'enyi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed…
We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to…
This work focuses on the problem of learning an unknown $3$-uniform hypergraph using edge-detecting queries. Our goal is to design a querying strategy that recovers the hyperedge set using as few queries as possible. We restrict our…
Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
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…
Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes…
The use of graph centrality measures applied to biological networks, such as protein interaction networks, underpins much research into identifying key players within biological processes. This approach however is restricted to dyadic…
Recently, research that focuses on the rigorous understanding of the relation between simulation and/or exact models on graphs and approximate counterparts has gained lots of momentum. This includes revisiting the performance of classic…
The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's…
In the qualitative theory of ordinary differential equations, we can find many papers whose objective is the classification of all the possible topological phase portraits of a given family of differential system. Most of the studies rely…
The integration of empirical data in computational frameworks to model the spread of infectious diseases poses challenges that are becoming pressing with the increasing availability of high-resolution information on human mobility and…