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Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to…

The spread of an infectious disease can be promoted by previous infections with other pathogens. This cooperative effect can give rise to violent outbreaks, reflecting the presence of an abrupt epidemic transition. As for other diffusive…

Chronic viral infections can persist in an infected person for decades. From the perspective of the virus, a single infection can span thousands of generations, leading to a highly diverse population of viruses with its own complex…

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms through which extinction of infection propagation comes about. We here report on a…

The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…

The structure of a network dramatically affects the spreading phenomena unfolding upon it. The contact distribution of the nodes has long been recognized as the key ingredient in influencing the outbreak events. However, limited knowledge…

The statistical field theory of information dynamics on complex networks concerns the dynamical evolution of large classes of models of complex systems. Previous work has focused on networks where nodes carry an information field, which…

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…

Coinfection is the process by which a host that is infected with a pathogen becomes infected by a second pathogen at a later point in time. An immunosuppressant host response to a primary disease can facilitate spreading of a subsequent…

Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…

We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence…

Network ecology is a rising field of quantitative biology representing ecosystems as complex networks. A suitable example is parasite spreading: several parasites may be transmitted among their hosts through different mechanisms, each one…

We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…

Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that…

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

Social networks are the prime channel for the spreading of computer viruses. Yet the study of their propagation neglects the temporal nature of social interactions and the heterogeneity of users' susceptibility. Here, we introduce a…