Related papers: Mean field at distance one
Infectious diseases often spread faster near their peak than would be predicted given early data on transmission. Despite the commonality of this phenomena, there are no known general mechanisms able to cause an exponentially spreading dis-…
Network--based epidemic models that account for heterogeneous contact patterns are extensively used to predict and control the diffusion of infectious diseases. We use census and survey data to reconstruct a geo--referenced and…
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and…
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…
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of $n>1$ agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with…
The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…
We model recruitment in adaptive social networks in the presence of birth and death processes. Recruitment is characterized by nodes changing their status to that of the recruiting class as a result of contact with recruiting nodes. Only a…
The analysis of networks affects the research of many real phenomena. The complex network structure can be viewed as a network's state at the time of the analysis or as a result of the process through which the network arises. Research…
Social networks have become ubiquitous in our daily life, as such it has attracted great research interests recently. A key challenge is that it is of extremely large-scale with tremendous information flow, creating the phenomenon of "Big…
Infectious pathogens often propagate by superspreading, which focusses onward transmission on disproportionately few infected individuals. At the same time, infector-infectee pairs tend to have more similar transmission potentials than…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced…