826 research outputs found
Modeling Infection with Multi-agent Dynamics
Developing the ability to comprehensively study infections in small
populations enables us to improve epidemic models and better advise individuals
about potential risks to their health. We currently have a limited
understanding of how infections spread within a small population because it has
been difficult to closely track an infection within a complete community. The
paper presents data closely tracking the spread of an infection centered on a
student dormitory, collected by leveraging the residents' use of cellular
phones. The data are based on daily symptom surveys taken over a period of four
months and proximity tracking through cellular phones. We demonstrate that
using a Bayesian, discrete-time multi-agent model of infection to model
real-world symptom reports and proximity tracking records gives us important
insights about infec-tions in small populations
Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach
We introduce a new method to efficiently approximate the number of infections
resulting from a given initially-infected node in a network of susceptible
individuals. Our approach is based on counting the number of possible infection
walks of various lengths to each other node in the network. We analytically
study the properties of our method, in particular demonstrating different forms
for SIS and SIR disease spreading (e.g. under the SIR model our method counts
self-avoiding walks). In comparison to existing methods to infer the spreading
efficiency of different nodes in the network (based on degree, k-shell
decomposition analysis and different centrality measures), our method directly
considers the spreading process and, as such, is unique in providing estimation
of actual numbers of infections. Crucially, in simulating infections on various
real-world networks with the SIR model, we show that our walks-based method
improves the inference of effectiveness of nodes over a wide range of infection
rates compared to existing methods. We also analyse the trade-off between
estimate accuracy and computational cost, showing that the better accuracy here
can still be obtained at a comparable computational cost to other methods.Comment: 6 page
Scaling laws for the movement of people between locations in a large city
Large scale simulations of the movements of people in a ``virtual'' city and
their analyses are used to generate new insights into understanding the dynamic
processes that depend on the interactions between people. Models, based on
these interactions, can be used in optimizing traffic flow, slowing the spread
of infectious diseases or predicting the change in cell phone usage in a
disaster. We analyzed cumulative and aggregated data generated from the
simulated movements of 1.6 million individuals in a computer (pseudo
agent-based) model during a typical day in Portland, Oregon. This city is
mapped into a graph with nodes representing physical locations such
as buildings. Connecting edges model individual's flow between nodes. Edge
weights are constructed from the daily traffic of individuals moving between
locations. The number of edges leaving a node (out-degree), the edge weights
(out-traffic), and the edge-weights per location (total out-traffic) are fitted
well by power law distributions. The power law distributions also fit subgraphs
based on work, school, and social/recreational activities. The resulting
weighted graph is a ``small world'' and has scaling laws consistent with an
underlying hierarchical structure. We also explore the time evolution of the
largest connected component and the distribution of the component sizes. We
observe a strong linear correlation between the out-degree and total
out-traffic distributions and significant levels of clustering. We discuss how
these network features can be used to characterize social networks and their
relationship to dynamic processes.Comment: 18 pages, 10 figure
A Mathematical Framework for Agent Based Models of Complex Biological Networks
Agent-based modeling and simulation is a useful method to study biological
phenomena in a wide range of fields, from molecular biology to ecology. Since
there is currently no agreed-upon standard way to specify such models it is not
always easy to use published models. Also, since model descriptions are not
usually given in mathematical terms, it is difficult to bring mathematical
analysis tools to bear, so that models are typically studied through
simulation. In order to address this issue, Grimm et al. proposed a protocol
for model specification, the so-called ODD protocol, which provides a standard
way to describe models. This paper proposes an addition to the ODD protocol
which allows the description of an agent-based model as a dynamical system,
which provides access to computational and theoretical tools for its analysis.
The mathematical framework is that of algebraic models, that is, time-discrete
dynamical systems with algebraic structure. It is shown by way of several
examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog
On the Computational Complexity of Measuring Global Stability of Banking Networks
Threats on the stability of a financial system may severely affect the
functioning of the entire economy, and thus considerable emphasis is placed on
the analyzing the cause and effect of such threats. The financial crisis in the
current and past decade has shown that one important cause of instability in
global markets is the so-called financial contagion, namely the spreading of
instabilities or failures of individual components of the network to other,
perhaps healthier, components. This leads to a natural question of whether the
regulatory authorities could have predicted and perhaps mitigated the current
economic crisis by effective computations of some stability measure of the
banking networks. Motivated by such observations, we consider the problem of
defining and evaluating stabilities of both homogeneous and heterogeneous
banking networks against propagation of synchronous idiosyncratic shocks given
to a subset of banks. We formalize the homogeneous banking network model of
Nier et al. and its corresponding heterogeneous version, formalize the
synchronous shock propagation procedures, define two appropriate stability
measures and investigate the computational complexities of evaluating these
measures for various network topologies and parameters of interest. Our results
and proofs also shed some light on the properties of topologies and parameters
of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic
Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many
statistics and machine learning applications ranging from support vector
machines to Gaussian processes and kernel embeddings of distributions.
Operators acting on such spaces are, for instance, required to embed
conditional probability distributions in order to implement the kernel Bayes
rule and build sequential data models. It was recently shown that transfer
operators such as the Perron-Frobenius or Koopman operator can also be
approximated in a similar fashion using covariance and cross-covariance
operators and that eigenfunctions of these operators can be obtained by solving
associated matrix eigenvalue problems. The goal of this paper is to provide a
solid functional analytic foundation for the eigenvalue decomposition of RKHS
operators and to extend the approach to the singular value decomposition. The
results are illustrated with simple guiding examples
Sensitivity of Household Transmission to Household Contact Structure and Size
Study the influence of household contact structure on the spread of an influenza-like illness. Examine whether changes to in-home care giving arrangements can significantly affect the household transmission counts.We simulate two different behaviors for the symptomatic person; either s/he remains at home in contact with everyone else in the household or s/he remains at home in contact with only the primary caregiver in the household. The two different cases are referred to as full mixing and single caregiver, respectively.The results show that the household's cumulative transmission count is lower in case of a single caregiver configuration than in the full mixing case. The household transmissions vary almost linearly with the household size in both single caregiver and full mixing cases. However the difference in household transmissions due to the difference in household structure grows with the household size especially in case of moderate flu.These results suggest that details about human behavior and household structure do matter in epidemiological models. The policy of home isolation of the sick has significant effect on the household transmission count depending upon the household size
Bayesian Best-Arm Identification for Selecting Influenza Mitigation Strategies
Pandemic influenza has the epidemic potential to kill millions of people.
While various preventive measures exist (i.a., vaccination and school
closures), deciding on strategies that lead to their most effective and
efficient use remains challenging. To this end, individual-based
epidemiological models are essential to assist decision makers in determining
the best strategy to curb epidemic spread. However, individual-based models are
computationally intensive and it is therefore pivotal to identify the optimal
strategy using a minimal amount of model evaluations. Additionally, as
epidemiological modeling experiments need to be planned, a computational budget
needs to be specified a priori. Consequently, we present a new sampling
technique to optimize the evaluation of preventive strategies using fixed
budget best-arm identification algorithms. We use epidemiological modeling
theory to derive knowledge about the reward distribution which we exploit using
Bayesian best-arm identification algorithms (i.e., Top-two Thompson sampling
and BayesGap). We evaluate these algorithms in a realistic experimental setting
and demonstrate that it is possible to identify the optimal strategy using only
a limited number of model evaluations, i.e., 2-to-3 times faster compared to
the uniform sampling method, the predominant technique used for epidemiological
decision making in the literature. Finally, we contribute and evaluate a
statistic for Top-two Thompson sampling to inform the decision makers about the
confidence of an arm recommendation
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