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Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between…
In this paper, we study the trajectory of a classic SIR epidemic on a family of dynamic random graphs of fixed size, whose set of edges continuously evolves over time. We set general infection and recovery times, and start the epidemic from…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected…
Information diffusion, spreading of infectious diseases, and spreading of rumors are fundamental processes occurring in real-life networks. In many practical cases, one can observe when nodes become infected, but the underlying network,…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and…
This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…
We examine the spread of an infectious disease, such as one that is caused by a respiratory virus, with two distinct modes of transmission. To do this, we consider a susceptible--infected--susceptible (SIS) disease on a hypergraph, which…
We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible…
Using the SIS model on unweighted and weighted networks, we consider the disease localization phenomenon. In contrast to the well-recognized point of view that diseases infect a finite fraction of vertices right above the epidemic…
Numerous approaches study the vulnerability of networks against social contagion. Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
Contagion processes on networks, including disease spreading, information diffusion, or social behaviors propagation, can be modeled as simple contagion, i.e. involving one connection at a time, or as complex contagion, in which multiple…
We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
A system to model the spread of COVID-19 cases after lockdown has been proposed, to define new preventive measures based on hotspots, using the graph clustering algorithm. This method allows for more lenient measures in areas less prone to…
Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…