4,557 research outputs found
Control of Time-Varying Epidemic-Like Stochastic Processes and Their Mean-Field Limits
The optimal control of epidemic-like stochastic processes is important both
historically and for emerging applications today, where it can be especially
important to include time-varying parameters that impact viral epidemic-like
propagation. We connect the control of such stochastic processes with
time-varying behavior to the stochastic shortest path problem and obtain
solutions for various cost functions. Then, under a mean-field scaling, this
general class of stochastic processes is shown to converge to a corresponding
dynamical system. We analogously establish that the optimal control of this
class of processes converges to the optimal control of the limiting dynamical
system. Consequently, we study the optimal control of the dynamical system
where the comparison of both controlled systems renders various important
mathematical properties of interest.Comment: arXiv admin note: substantial text overlap with arXiv:1709.0798
Analytical computation of the epidemic threshold on temporal networks
The time variation of contacts in a networked system may fundamentally alter
the properties of spreading processes and affect the condition for large-scale
propagation, as encoded in the epidemic threshold. Despite the great interest
in the problem for the physics, applied mathematics, computer science and
epidemiology communities, a full theoretical understanding is still missing and
currently limited to the cases where the time-scale separation holds between
spreading and network dynamics or to specific temporal network models. We
consider a Markov chain description of the Susceptible-Infectious-Susceptible
process on an arbitrary temporal network. By adopting a multilayer perspective,
we develop a general analytical derivation of the epidemic threshold in terms
of the spectral radius of a matrix that encodes both network structure and
disease dynamics. The accuracy of the approach is confirmed on a set of
temporal models and empirical networks and against numerical results. In
addition, we explore how the threshold changes when varying the overall time of
observation of the temporal network, so as to provide insights on the optimal
time window for data collection of empirical temporal networked systems. Our
framework is both of fundamental and practical interest, as it offers novel
understanding of the interplay between temporal networks and spreading
dynamics.Comment: 22 pages, 6 figure
Human mobility networks and persistence of rapidly mutating pathogens
Rapidly mutating pathogens may be able to persist in the population and reach
an endemic equilibrium by escaping hosts' acquired immunity. For such diseases,
multiple biological, environmental and population-level mechanisms determine
the dynamics of the outbreak, including pathogen's epidemiological traits (e.g.
transmissibility, infectious period and duration of immunity), seasonality,
interaction with other circulating strains and hosts' mixing and spatial
fragmentation. Here, we study a susceptible-infected-recovered-susceptible
model on a metapopulation where individuals are distributed in subpopulations
connected via a network of mobility flows. Through extensive numerical
simulations, we explore the phase space of pathogen's persistence and map the
dynamical regimes of the pathogen following emergence. Our results show that
spatial fragmentation and mobility play a key role in the persistence of the
disease whose maximum is reached at intermediate mobility values. We describe
the occurrence of different phenomena including local extinction and emergence
of epidemic waves, and assess the conditions for large scale spreading.
Findings are highlighted in reference to previous works and to real scenarios.
Our work uncovers the crucial role of hosts' mobility on the ecological
dynamics of rapidly mutating pathogens, opening the path for further studies on
disease ecology in the presence of a complex and heterogeneous environment.Comment: 29 pages, 7 figures. Submitted for publicatio
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Capturing the time-varying drivers of an epidemic using stochastic dynamical systems
Epidemics are often modelled using non-linear dynamical systems observed
through partial and noisy data. In this paper, we consider stochastic
extensions in order to capture unknown influences (changing behaviors, public
interventions, seasonal effects etc). These models assign diffusion processes
to the time-varying parameters, and our inferential procedure is based on a
suitably adjusted adaptive particle MCMC algorithm. The performance of the
proposed computational methods is validated on simulated data and the adopted
model is applied to the 2009 H1N1 pandemic in England. In addition to
estimating the effective contact rate trajectories, the methodology is applied
in real time to provide evidence in related public health decisions. Diffusion
driven SEIR-type models with age structure are also introduced.Comment: 21 pages, 5 figure
Spreading processes in Multilayer Networks
Several systems can be modeled as sets of interconnected networks or networks
with multiple types of connections, here generally called multilayer networks.
Spreading processes such as information propagation among users of an online
social networks, or the diffusion of pathogens among individuals through their
contact network, are fundamental phenomena occurring in these networks.
However, while information diffusion in single networks has received
considerable attention from various disciplines for over a decade, spreading
processes in multilayer networks is still a young research area presenting many
challenging research issues. In this paper we review the main models, results
and applications of multilayer spreading processes and discuss some promising
research directions.Comment: 21 pages, 3 figures, 4 table
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
An Agent-Based Spatially Explicit Epidemiological Model in MASON
This paper outlines the design and implementation of an agent-based epidemiological simulation system. The system was implemented in the MASON toolkit, a set of Java-based agent-simulation libraries. This epidemiological simulation system is robust and extensible for multiple applications, including classroom demonstrations of many types of epidemics and detailed numerical experimentation on a particular disease. The application has been made available as an applet on the MASON web site, and as source code on the author\'s web site.Epidemiology, Social Networks, Agent-Based Simulation, MASON Toolkit
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