8,682 research outputs found
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
Moment Closure - A Brief Review
Moment closure methods appear in myriad scientific disciplines in the
modelling of complex systems. The goal is to achieve a closed form of a large,
usually even infinite, set of coupled differential (or difference) equations.
Each equation describes the evolution of one "moment", a suitable
coarse-grained quantity computable from the full state space. If the system is
too large for analytical and/or numerical methods, then one aims to reduce it
by finding a moment closure relation expressing "higher-order moments" in terms
of "lower-order moments". In this brief review, we focus on highlighting how
moment closure methods occur in different contexts. We also conjecture via a
geometric explanation why it has been difficult to rigorously justify many
moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in
mathematics, physics, chemistry and quantitative biolog
Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model
Data of physical contacts and face-to-face communications suggest temporally
varying networks as the media on which infections take place among humans and
animals. Epidemic processes on temporal networks are complicated by complexity
of both network structure and temporal dimensions. Theoretical approaches are
much needed for identifying key factors that affect dynamics of epidemics. In
particular, what factors make some temporal networks stronger media of
infection than other temporal networks is under debate. We develop a theory to
understand the susceptible-infected-susceptible epidemic model on arbitrary
temporal networks, where each contact is used for a finite duration. We show
that temporality of networks lessens the epidemic threshold such that
infections persist more easily in temporal networks than in their static
counterparts. We further show that the Lie commutator bracket of the adjacency
matrices at different times is a key determinant of the epidemic threshold in
temporal networks. The effect of temporality on the epidemic threshold, which
depends on a data set, is approximately predicted by the magnitude of a
commutator norm.Comment: 8 figures, 1 tabl
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models
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