7,038 research outputs found
A general class of spreading processes with non-Markovian dynamics
In this paper we propose a general class of models for spreading processes we
call the model. Unlike many works that consider a fixed number of
compartmental states, we allow an arbitrary number of states on arbitrary
graphs with heterogeneous parameters for all nodes and edges. As a result, this
generalizes an extremely large number of models studied in the literature
including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS
models. Furthermore, we show how the model allows us to model
non-Poisson spreading processes letting us capture much more complicated
dynamics than existing works such as information spreading through social
networks or the delayed incubation period of a disease like Ebola. This is in
contrast to the overwhelming majority of works in the literature that only
consider spreading processes that can be captured by a Markov process. After
developing the stochastic model, we analyze its deterministic mean-field
approximation and provide conditions for when the disease-free equilibrium is
stable. Simulations illustrate our results
Mathematical Modeling of Trending Topics on Twitter
Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses information spread, presents case studies pertaining to the prevalence of several “trending” topics on Twitter over time. The study introduces a framework to compare information dynamics on Twitter based on the topical area as well as a framework for the prediction of topic prevalence. Additionally, methodological and results-based comparisons are drawn between the spread of information and the spread of infectious disease
Network Inoculation: Heteroclinics and phase transitions in an epidemic model
In epidemiological modelling, dynamics on networks, and in particular
adaptive and heterogeneous networks have recently received much interest. Here
we present a detailed analysis of a previously proposed model that combines
heterogeneity in the individuals with adaptive rewiring of the network
structure in response to a disease. We show that in this model qualitative
changes in the dynamics occur in two phase transitions. In a macroscopic
description one of these corresponds to a local bifurcation whereas the other
one corresponds to a non-local heteroclinic bifurcation. This model thus
provides a rare example of a system where a phase transition is caused by a
non-local bifurcation, while both micro- and macro-level dynamics are
accessible to mathematical analysis. The bifurcation points mark the onset of a
behaviour that we call network inoculation. In the respective parameter region
exposure of the system to a pathogen will lead to an outbreak that collapses,
but leaves the network in a configuration where the disease cannot reinvade,
despite every agent returning to the susceptible class. We argue that this
behaviour and the associated phase transitions can be expected to occur in a
wide class of models of sufficient complexity.Comment: 26 pages, 11 figure
Complex network analysis and nonlinear dynamics
This chapter aims at reviewing complex network and nonlinear dynamical
models and methods that were either developed for or applied to socioeconomic
issues, and pertinent to the theme of New Economic Geography. After an introduction
to the foundations of the field of complex networks, the present summary
introduces some applications of complex networks to economics, finance, epidemic
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issue
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