26,104 research outputs found
Group-based susceptible-infectious-susceptible model in large-scale directed networks
© 2019 Xu Wang et al. Epidemic models trade the modeling accuracy for complexity reduction. This paper proposes to group vertices in directed graphs based on connectivity and carries out epidemic spread analysis on the group basis, thereby substantially reducing the modeling complexity while preserving the modeling accuracy. A group-based continuous-time Markov SIS model is developed. The adjacency matrix of the network is also collapsed according to the grouping, to evaluate the Jacobian matrix of the group-based continuous-time Markov model. By adopting the mean-field approximation on the groups of nodes and links, the model complexity is significantly reduced as compared with previous topological epidemic models. An epidemic threshold is deduced based on the spectral radius of the collapsed adjacency matrix. The epidemic threshold is proved to be dependent on network structure and interdependent of the network scale. Simulation results validate the analytical epidemic threshold and confirm the asymptotical accuracy of the proposed epidemic model
A Comparative Analysis of Influenza Vaccination Programs
The threat of avian influenza and the 2004-2005 influenza vaccine supply
shortage in the United States has sparked a debate about optimal vaccination
strategies to reduce the burden of morbidity and mortality caused by the
influenza virus. We present a comparative analysis of two classes of suggested
vaccination strategies: mortality-based strategies that target high risk
populations and morbidity-based that target high prevalence populations.
Applying the methods of contact network epidemiology to a model of disease
transmission in a large urban population, we evaluate the efficacy of these
strategies across a wide range of viral transmission rates and for two
different age-specific mortality distributions. We find that the optimal
strategy depends critically on the viral transmission level (reproductive rate)
of the virus: morbidity-based strategies outperform mortality-based strategies
for moderately transmissible strains, while the reverse is true for highly
transmissible strains. These results hold for a range of mortality rates
reported for prior influenza epidemics and pandemics. Furthermore, we show that
vaccination delays and multiple introductions of disease into the community
have a more detrimental impact on morbidity-based strategies than
mortality-based strategies. If public health officials have reasonable
estimates of the viral transmission rate and the frequency of new introductions
into the community prior to an outbreak, then these methods can guide the
design of optimal vaccination priorities. When such information is unreliable
or not available, as is often the case, this study recommends mortality-based
vaccination priorities
Networks and the epidemiology of infectious disease
The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues
Invited review: Epidemics on social networks
Since its first formulations almost a century ago, mathematical models for
disease spreading contributed to understand, evaluate and control the epidemic
processes.They promoted a dramatic change in how epidemiologists thought of the
propagation of infectious diseases.In the last decade, when the traditional
epidemiological models seemed to be exhausted, new types of models were
developed.These new models incorporated concepts from graph theory to describe
and model the underlying social structure.Many of these works merely produced a
more detailed extension of the previous results, but some others triggered a
completely new paradigm in the mathematical study of epidemic processes. In
this review, we will introduce the basic concepts of epidemiology, epidemic
modeling and networks, to finally provide a brief description of the most
relevant results in the field.Comment: 17 pages, 13 figure
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
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
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