1,175 research outputs found
Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
The surveillance, analysis and ultimately the efficient long-term prediction
and control of epidemic dynamics appear to be one of the major challenges
nowadays. Detailed atomistic mathematical models play an important role towards
this aim. In this work it is shown how one can exploit the Equation Free
approach and optimization methods such as Simulated Annealing to bridge
detailed individual-based epidemic simulation with coarse-grained,
systems-level, analysis. The methodology provides a systematic approach for
analyzing the parametric behavior of complex/ multi-scale epidemic simulators
much more efficiently than simply simulating forward in time. It is shown how
steady state and (if required) time-dependent computations, stability
computations, as well as continuation and numerical bifurcation analysis can be
performed in a straightforward manner. The approach is illustrated through a
simple individual-based epidemic model deploying on a random regular connected
graph. Using the individual-based microscopic simulator as a black box
coarse-grained timestepper and with the aid of Simulated Annealing I compute
the coarse-grained equilibrium bifurcation diagram and analyze the stability of
the stationary states sidestepping the necessity of obtaining explicit closures
at the macroscopic level under a pairwise representation perspective
Phase transitions in contagion processes mediated by recurrent mobility patterns
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 and recurrent flows and poorly modeled by the random diffusive
dynamics generally used to study them. Here we develop a theoretical framework
to analyze contagion within a network of locations where individuals recall
their geographic origins. We find a phase transition between a regime in which
the contagion affects a large fraction of the system and one in which only a
small fraction is affected. This transition cannot be uncovered by continuous
deterministic models due to the stochastic features of the contagion process
and defines an invasion threshold that depends on mobility parameters,
providing guidance for controlling contagion spread by constraining mobility
processes. We recover the threshold behavior by analyzing diffusion processes
mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary
Information; Nature Physics (2011
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Modeling epidemics on adaptively evolving networks: a data-mining perspective
The exploration of epidemic dynamics on dynamically evolving ("adaptive")
networks poses nontrivial challenges to the modeler, such as the determination
of a small number of informative statistics of the detailed network state (that
is, a few "good observables") that usefully summarize the overall (macroscopic,
systems level) behavior. Trying to obtain reduced, small size, accurate models
in terms of these few statistical observables - that is, coarse-graining the
full network epidemic model to a small but useful macroscopic one - is even
more daunting. Here we describe a data-based approach to solving the first
challenge: the detection of a few informative collective observables of the
detailed epidemic dynamics. This will be accomplished through Diffusion Maps, a
recently developed data-mining technique. We illustrate the approach through
simulations of a simple mathematical model of epidemics on a network: a model
known to exhibit complex temporal dynamics. We will discuss potential
extensions of the approach, as well as possible shortcomings.Comment: 24 pages, 8 figures, submitted to Virulenc
Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model
We show how appropriate rewiring with the aid of Metropolis Monte Carlo
computational experiments can be exploited to create network topologies
possessing prescribed values of the average path length (APL) while keeping the
same connectivity degree and clustering coefficient distributions. Using the
proposed rewiring rules we illustrate how the emergent dynamics of the
celebrated majority-rule model are shaped by the distinct impact of the APL
attesting the need for developing efficient algorithms for tuning such network
characteristics.Comment: 10 figure
Recommended from our members
Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone.
Dynamic SEIR (Susceptible, Exposed, Infectious, Removed) compartmental models provide a tool for predicting the size and duration of both unfettered and managed outbreaks-the latter in the context of interventions such as case detection, patient isolation, vaccination and treatment. The reliability of this tool depends on the validity of key assumptions that include homogeneity of individuals and spatio-temporal homogeneity. Although the SEIR compartmental framework can easily be extended to include demographic (e.g. age) and additional disease (e.g. healthcare workers) classes, dependence of transmission rates on time, and metapopulation structure, fitting such extended models is hampered by both a proliferation of free parameters and insufficient or inappropriate data. This raises the question of how effective a tool the basic SEIR framework may actually be. We go some way here to answering this question in the context of the 2014-2015 outbreak of Ebola in West Africa by comparing fits of an SEIR time-dependent transmission model to both country- and district-level weekly incidence data. Our novel approach in estimating the effective-size-of-the-populations-at-risk ( Neff) and initial number of exposed individuals ( E0) at both district and country levels, as well as the transmission function parameters, including a time-to-halving-the-force-of-infection ( tf/2) parameter, provides new insights into this Ebola outbreak. It reveals that the estimate R0 â 1.7 from country-level data appears to seriously underestimate R0 â 3.3 - 4.3 obtained from more spatially homogeneous district-level data. Country-level data also overestimate tf/2 â 22 weeks, compared with 8-10 weeks from district-level data. Additionally, estimates for the duration of individual infectiousness is around two weeks from spatially inhomogeneous country-level data compared with 2.4-4.5 weeks from spatially more homogeneous district-level data, which estimates are rather high compared with most values reported in the literature. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'
Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data
Complex system simulation has been playing an irreplaceable role in
understanding, predicting, and controlling diverse complex systems. In the past
few decades, the multi-scale simulation technique has drawn increasing
attention for its remarkable ability to overcome the challenges of complex
system simulation with unknown mechanisms and expensive computational costs. In
this survey, we will systematically review the literature on multi-scale
simulation of complex systems from the perspective of knowledge and data.
Firstly, we will present background knowledge about simulating complex system
simulation and the scales in complex systems. Then, we divide the main
objectives of multi-scale modeling and simulation into five categories by
considering scenarios with clear scale and scenarios with unclear scale,
respectively. After summarizing the general methods for multi-scale simulation
based on the clues of knowledge and data, we introduce the adopted methods to
achieve different objectives. Finally, we introduce the applications of
multi-scale simulation in typical matter systems and social systems
Activity driven modeling of time varying networks
Network modeling plays a critical role in identifying statistical
regularities and structural principles common to many systems. The large
majority of recent modeling approaches are connectivity driven. The structural
patterns of the network are at the basis of the mechanisms ruling the network
formation. Connectivity driven models necessarily provide a time-aggregated
representation that may fail to describe the instantaneous and fluctuating
dynamics of many networks. We address this challenge by defining the activity
potential, a time invariant function characterizing the agents' interactions
and constructing an activity driven model capable of encoding the instantaneous
time description of the network dynamics. The model provides an explanation of
structural features such as the presence of hubs, which simply originate from
the heterogeneous activity of agents. Within this framework, highly dynamical
networks can be described analytically, allowing a quantitative discussion of
the biases induced by the time-aggregated representations in the analysis of
dynamical processes.Comment: 10 pages, 4 figure
- âŠ