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A Computational Simulation Model for Predicting Infectious Disease Spread using the Evolving Contact Network Algorithm
Commonly used simulation models for predicting outbreaks of re-emerging infectious diseases (EIDs) take an individual-level or a population-level approach to modeling contact dynamics. These approaches are a trade-off between the ability to incorporate individual-level dynamics and computational efficiency. Agent-based network models (ABNM) use an individual-level approach by simulating the entire population and its contact structure, which increases the ability of adding detailed individual-level characteristics. However, as this method is computationally expensive, ABNMs use scaled-down versions of the full population, which are unsuitable for low prevalence diseases as the number of infected cases would become negligible during scaling-down. Compartmental models use differential equations to simulate population-level features, which is computationally inexpensive and can model full-scale populations. However, as the compartmental model framework assumes random mixing between people, it is not suitable for diseases where the underlying contact structures are a significant feature of disease epidemiology. Therefore, current methods are unsuitable for simulating diseases that have low prevalence and where the contact structures are significant.
The conceptual framework for a new simulation method, Evolving Contact Network Algorithm (ECNA), was recently proposed to address the above gap. The ECNA combines the attributes of ABNM and compartmental modeling. It generates a contact network of only infected persons and their immediate contacts, and evolves the network as new persons become infected.
The conceptual framework of the ECNA is promising for application to diseases with low prevalence and where contact structures are significant. This thesis develops and tests different algorithms to advance the computational capabilities of the ECNA and its flexibility to model different network settings. These features are key components that determine the feasibility of ECNA for application to disease prediction. Results indicate that the ECNA is nearly 20 times faster than ABNM when simulating a population of size 150,000 and flexible for modeling networks with two contact layers and communities. Considering uncertainties in epidemiological features and origin of future EIDs, there is a significant need for a computationally efficient method that is suitable for analyses of a range of potential EIDs at a global scale. This work holds promise towards the development of such a model
Multifractal Network Generator
We introduce a new approach to constructing networks with realistic features.
Our method, in spite of its conceptual simplicity (it has only two parameters)
is capable of generating a wide variety of network types with prescribed
statistical properties, e.g., with degree- or clustering coefficient
distributions of various, very different forms. In turn, these graphs can be
used to test hypotheses, or, as models of actual data. The method is based on a
mapping between suitably chosen singular measures defined on the unit square
and sparse infinite networks. Such a mapping has the great potential of
allowing for graph theoretical results for a variety of network topologies. The
main idea of our approach is to go to the infinite limit of the singular
measure and the size of the corresponding graph simultaneously. A very unique
feature of this construction is that the complexity of the generated network is
increasing with the size. We present analytic expressions derived from the
parameters of the -- to be iterated-- initial generating measure for such major
characteristics of graphs as their degree, clustering coefficient and
assortativity coefficient distributions. The optimal parameters of the
generating measure are determined from a simple simulated annealing process.
Thus, the present work provides a tool for researchers from a variety of fields
(such as biology, computer science, biology, or complex systems) enabling them
to create a versatile model of their network data.Comment: Preprint. Final version appeared in PNAS
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
Learning multifractal structure in large networks
Generating random graphs to model networks has a rich history. In this paper,
we analyze and improve upon the multifractal network generator (MFNG)
introduced by Palla et al. We provide a new result on the probability of
subgraphs existing in graphs generated with MFNG. From this result it follows
that we can quickly compute moments of an important set of graph properties,
such as the expected number of edges, stars, and cliques. Specifically, we show
how to compute these moments in time complexity independent of the size of the
graph and the number of recursive levels in the generative model. We leverage
this theory to a new method of moments algorithm for fitting large networks to
MFNG. Empirically, this new approach effectively simulates properties of
several social and information networks. In terms of matching subgraph counts,
our method outperforms similar algorithms used with the Stochastic Kronecker
Graph model. Furthermore, we present a fast approximation algorithm to generate
graph instances following the multi- fractal structure. The approximation
scheme is an improvement over previous methods, which ran in time complexity
quadratic in the number of vertices. Combined, our method of moments and fast
sampling scheme provide the first scalable framework for effectively modeling
large networks with MFNG
Large deviations of cascade processes on graphs
Simple models of irreversible dynamical processes such as Bootstrap
Percolation have been successfully applied to describe cascade processes in a
large variety of different contexts. However, the problem of analyzing
non-typical trajectories, which can be crucial for the understanding of the
out-of-equilibrium phenomena, is still considered to be intractable in most
cases. Here we introduce an efficient method to find and analyze optimized
trajectories of cascade processes. We show that for a wide class of
irreversible dynamical rules, this problem can be solved efficiently on
large-scale systems
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
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