21 research outputs found
Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks
Numerical simulation of continuous-time Markovian processes is an essential
and widely applied tool in the investigation of epidemic spreading on complex
networks. Due to the high heterogeneity of the connectivity structure through
which epidemics is transmitted, efficient and accurate implementations of
generic epidemic processes are not trivial and deviations from statistically
exact prescriptions can lead to uncontrolled biases. Based on the Gillespie
algorithm (GA), in which only steps that change the state are considered, we
develop numerical recipes and describe their computer implementations for
statistically exact and computationally efficient simulations of generic
Markovian epidemic processes aiming at highly heterogeneous and large networks.
The central point of the recipes investigated here is to include phantom
processes, that do not change the states but do count for time increments. We
compare the efficiencies for the susceptible-infected-susceptible, contact
process and susceptible-infected-recovered models, that are particular cases of
a generic model considered here. We numerically confirm that the simulation
outcomes of the optimized algorithms are statistically indistinguishable from
the original GA and can be several orders of magnitude more efficient.Comment: 12 pages, 9 figure
Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
We provide numerical evidence for slow dynamics of the
susceptible-infected-susceptible model evolving on finite-size random networks
with power-law degree distributions. Extensive simulations were done by
averaging the activity density over many realizations of networks. We
investigated the effects of outliers in both highly fluctuating (natural
cutoff) and non-fluctuating (hard cutoff) most connected vertices. Logarithmic
and power-law decays in time were found for natural and hard cutoffs,
respectively. This happens in extended regions of the control parameter space
, suggesting Griffiths effects, induced by the
topological inhomogeneities. Optimal fluctuation theory considering
sample-to-sample fluctuations of the pseudo thresholds is presented to explain
the observed slow dynamics. A quasistationary analysis shows that response
functions remain bounded at . We argue these to be signals of a
smeared transition. However, in the thermodynamic limit the Griffiths effects
loose their relevancy and have a conventional critical point at .
Since many real networks are composed by heterogeneous and weakly connected
modules, the slow dynamics found in our analysis of independent and finite
networks can play an important role for the deeper understanding of such
systems.Comment: 10 pages, 8 figure
Griffiths phases in infinite-dimensional, non-hierarchical modular networks
Griffiths phases (GPs), generated by the heterogeneities on modular networks,
have recently been suggested to provide a mechanism, rid of fine parameter
tuning, to explain the critical behavior of complex systems. One conjectured
requirement for systems with modular structures was that the network of modules
must be hierarchically organized and possess finite dimension. We investigate
the dynamical behavior of an activity spreading model, evolving on
heterogeneous random networks with highly modular structure and organized
non-hierarchically. We observe that loosely coupled modules act as effective
rare-regions, slowing down the extinction of activation. As a consequence, we
find extended control parameter regions with continuously changing dynamical
exponents for single network realizations, preserved after finite size
analyses, as in a real GP. The avalanche size distributions of spreading events
exhibit robust power-law tails. Our findings relax the requirement of
hierarchical organization of the modular structure, which can help to
rationalize the criticality of modular systems in the framework of GPs.Comment: 14 pages, 8 figure
Quantifying echo chamber effects in information spreading over political communication networks
Echo chambers in online social networks, in which users prefer to interact
only with ideologically-aligned peers, are believed to facilitate
misinformation spreading and contribute to radicalize political discourse. In
this paper, we gauge the effects of echo chambers in information spreading
phenomena over political communication networks. Mining 12 million Twitter
messages, we reconstruct a network in which users interchange opinions related
to the impeachment of the former Brazilian President Dilma Rousseff. We define
a continuous {political position} parameter, independent of the network's
structure, that allows to quantify the presence of echo chambers in the
strongly connected component of the network, reflected in two well-separated
communities of similar sizes with opposite views of the impeachment process. By
means of simple spreading models, we show that the capability of users in
propagating the content they produce, measured by the associated spreadability,
strongly depends on their attitude. Users expressing pro-impeachment sentiments
are capable to transmit information, on average, to a larger audience than
users expressing anti-impeachment sentiments. Furthermore, the users'
spreadability is correlated to the diversity, in terms of political position,
of the audience reached. Our method can be exploited to identify the presence
of echo chambers and their effects across different contexts and shed light
upon the mechanisms allowing to break echo chambers.Comment: 9 pages, 4 figures. Supplementary Information available as ancillary
fil
Griffiths phases in infinite-dimensional, non-hierarchical modular networks
Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically. We observe that loosely coupled modules act as effective rare-regions, slowing down the extinction of activation. As a consequence, we find extended control parameter regions with continuously changing dynamical exponents for single network realizations, preserved after finite size analyses, as in a real GP. The avalanche size distributions of spreading events exhibit robust power-law tails. Our findings relax the requirement of hierarchical organization of the modular structure, which can help to rationalize the criticality of modular systems in the framework of GPs
Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
We analyze two alterations of the standard susceptible-infected-susceptible
(SIS) dynamics that preserve the central properties of spontaneous healing and
infection capacity of a vertex increasing unlimitedly with its degree. All
models have the same epidemic thresholds in mean-field theories but depending
on the network properties, simulations yield a dual scenario, in which the
epidemic thresholds of the modified SIS models can be either dramatically
altered or remain unchanged in comparison with the standard dynamics. For
uncorrelated synthetic networks having a power-law degree distribution with
exponent , the SIS dynamics are robust exhibiting essentially the
same outcomes for all investigated models. A threshold in better agreement with
the heterogeneous rather than quenched mean-field theory is observed in the
modified dynamics for exponent . Differences are more remarkable
for where a finite threshold is found in the modified models in
contrast with the vanishing threshold of the original one. This duality is
elucidated in terms of epidemic lifespan on star graphs. We verify that the
activation of the modified SIS models is triggered in the innermost component
of the network given by a -core decomposition for while it
happens only for , the
activation in the modified dynamics is collective involving essentially the
whole network while it is triggered by hubs in the standard SIS. The duality
also appears in the finite-size scaling of the critical quantities where
mean-field behaviors are observed for the modified, but not for the original
dynamics. Our results feed the discussions about the most proper conceptions of
epidemic models to describe real systems and the choices of the most suitable
theoretical approaches to deal with these models.Comment: 13 pages, 8 figure
Modeling communicable diseases, human mobility, and epidemics: a review
The spatiotemporal propagation patterns of recent infectious diseases, originated as localized epidemic outbreaks and eventually becoming global pandemics, are highly influenced by human mobility. Case exportation from endemic areas to the rest of the countries has become unavoidable because of the striking growth of the global mobility network, helping to overcome the physical distance existing between faraway regions. In this context, understanding the features driving contagions upon the arrival of an index case in local environments constitutes an essential task to devise policies aimed at avoiding the community transmission of these diseases and the subsequent case exportation to other unaffected areas. In this review, an overview of the different models addressing this topic is given, focusing on the movement–interaction–return model and different subsequent frameworks introduced to explain the complex interplay between the recurrent movements and contagion dynamics
Monitorando o número de casos e óbitos por COVID-19 no Brasil em nível munipal e de unidades federativas
We present a dataset containing the reported number of COVID-19 cases and deaths at municipal and federative units level in Brazil. Data is aggregated daily from official sources with the most updated numbers, providing a reliable, free and simple resource for researchers, health authorities and general public. Interactive pages in English and Portuguese are available, containing maps, graphs and tables with all the data. Data about recovered, suspected and tests made are also available for most federative units.Apresentamos um banco de dados contendo o número de casos e óbitos reportados por COVID-19 no Brasil em nível municipal e de unidades federativas. Os dados são agregados diariamente a partir de fontes oficiais com os números mais atualizados, disponibilizando um recurso confiável, livre e simples para pesquisadores, autoridades desaúde e o público geral. Páginas interativas em inglês e português estão disponíveis, contendo mapa, gráficos e tabelas com todos os dados. Dados sobre recuperados, suspeitos e testes realizados também estão disponíveis para a maioria das unidades federativas