1,415 research outputs found
Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been shown that network heterogeneity, i.e. a broad degree distribution, can lower the epidemic threshold at which epidemics can invade the system. Network heterogeneity can thus allow diseases with lower transmission probabilities to persist and spread. However, it has been pointed out that networks in which the properties of nodes are intrinsically heterogeneous can be very resilient to disease spreading. Heterogeneity in structure can enhance or diminish the resilience of networks with heterogeneous nodes, depending on the correlations between the topological and intrinsic properties. Here, we consider a plausible scenario where people have intrinsic differences in susceptibility and adapt their social network structure to the presence of the disease. We show that the resilience of networks with heterogeneous connectivity can surpass those of networks with homogeneous connectivity. For epidemiology, this implies that network heterogeneity should not be studied in isolation, it is instead the heterogeneity of infection risk that determines the likelihood of outbreaks
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Phase Transitions and Criticality in the Collective Behavior of Animals -- Self-organization and biological function
Collective behaviors exhibited by animal groups, such as fish schools, bird
flocks, or insect swarms are fascinating examples of self-organization in
biology. Concepts and methods from statistical physics have been used to argue
theoretically about the potential consequences of collective effects in such
living systems. In particular, it has been proposed that such collective
systems should operate close to a phase transition, specifically a
(pseudo-)critical point, in order to optimize their capability for collective
computation. In this chapter, we will first review relevant phase transitions
exhibited by animal collectives, pointing out the difficulties of applying
concepts from statistical physics to biological systems. Then we will discuss
the current state of research on the "criticality hypothesis", including
methods for how to measure distance from criticality and specific functional
consequences for animal groups operating near a phase transition. We will
highlight the emerging view that de-emphasizes the optimality of being exactly
at a critical point and instead explores the potential benefits of living
systems being able to tune to an optimal distance from criticality. We will
close by laying out future challenges for studying collective behavior at the
interface of physics and biology.Comment: to appear in "Order, disorder, and criticality", vol. VII, World
Scientific Publishin
Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks
The colocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts which typically occur through environments like workplaces, restaurants, and households; and by (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, super-exponential spread, and hysteresis
Social contagion models on hypergraphs
Our understanding of the dynamics of complex networked systems has increased
significantly in the last two decades. However, most of our knowledge is built
upon assuming pairwise relations among the system's components. This is often
an oversimplification, for instance, in social interactions that occur
frequently within groups. To overcome this limitation, here we study the
dynamics of social contagion on hypergraphs. We develop an analytical framework
and provide numerical results for arbitrary hypergraphs, which we also support
with Monte Carlo simulations. Our analyses show that the model has a vast
parameter space, with first and second-order transitions, bi-stability, and
hysteresis. Phenomenologically, we also extend the concept of latent heat to
social contexts, which might help understanding oscillatory social behaviors.
Our work unfolds the research line of higher-order models and the analytical
treatment of hypergraphs, posing new questions and paving the way for modeling
dynamical processes on these networks.Comment: 17 pages, including 14 figure
Invited review: Epidemics on social networks
Since its first formulations almost a century ago, mathematical models for
disease spreading contributed to understand, evaluate and control the epidemic
processes.They promoted a dramatic change in how epidemiologists thought of the
propagation of infectious diseases.In the last decade, when the traditional
epidemiological models seemed to be exhausted, new types of models were
developed.These new models incorporated concepts from graph theory to describe
and model the underlying social structure.Many of these works merely produced a
more detailed extension of the previous results, but some others triggered a
completely new paradigm in the mathematical study of epidemic processes. In
this review, we will introduce the basic concepts of epidemiology, epidemic
modeling and networks, to finally provide a brief description of the most
relevant results in the field.Comment: 17 pages, 13 figure
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