3,165 research outputs found
Robust oscillations in SIS epidemics on adaptive networks: Coarse-graining by automated moment closure
We investigate the dynamics of an epidemiological
susceptible-infected-susceptible (SIS) model on an adaptive network. This model
combines epidemic spreading (dynamics on the network) with rewiring of network
connections (topological evolution of the network). We propose and implement a
computational approach that enables us to study the dynamics of the network
directly on an emergent, coarse-grained level. The approach sidesteps the
derivation of closed low-dimensional approximations. Our investigations reveal
that global coupling, which enters through the awareness of the population to
the disease, can result in robust large-amplitude oscillations of the state and
topology of the network.Comment: revised version 6 pages, 4 figure
Calculation of disease dynamics in a population of households
Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-suscep​tible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks
Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models
We demonstrate how direct simulation of stochastic, individual-based models
can be combined with continuum numerical analysis techniques to study the
dynamics of evolving diseases. % Sidestepping the necessity of obtaining
explicit population-level models, the approach analyzes the (unavailable in
closed form) `coarse' macroscopic equations, estimating the necessary
quantities through appropriately initialized, short `bursts' of
individual-based dynamic simulation. % We illustrate this approach by analyzing
a stochastic and discrete model for the evolution of disease agents caused by
point mutations within individual hosts. % Building up from classical SIR and
SIRS models, our example uses a one-dimensional lattice for variant space, and
assumes a finite number of individuals. % Macroscopic computational tasks
enabled through this approach include stationary state computation, coarse
projective integration, parametric continuation and stability analysis.Comment: 16 pages, 8 figure
Exact and approximate moment closures for non-Markovian network epidemics
Moment-closure techniques are commonly used to generate low-dimensional
deterministic models to approximate the average dynamics of stochastic systems
on networks. The quality of such closures is usually difficult to asses and the
relationship between model assumptions and closure accuracy are often
difficult, if not impossible, to quantify. Here we carefully examine some
commonly used moment closures, in particular a new one based on the concept of
maximum entropy, for approximating the spread of epidemics on networks by
reconstructing the probability distributions over triplets based on those over
pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under
Markovian and non-Markovian assumption characterising the latent and infectious
periods. We initially study two special networks, namely the open triplet and
closed triangle, for which we can obtain analytical results. We then explore
numerically the exactness of moment closures for a wide range of larger motifs,
thus gaining understanding of the factors that introduce errors in the
approximations, in particular the presence of a random duration of the
infectious period and the presence of overlapping triangles in a network. We
also derive a simpler and more intuitive proof than previously available
concerning the known result that pair-based moment closure is exact for the
Markovian SIR model on tree-like networks under pure initial conditions. We
also extend such a result to all infectious models, Markovian and
non-Markovian, in which susceptibles escape infection independently from each
infected neighbour and for which infectives cannot regain susceptible status,
provided the network is tree-like and initial conditions are pure. This works
represent a valuable step in deepening understanding of the assumptions behind
moment closure approximations and for putting them on a more rigorous
mathematical footing.Comment: Main text (45 pages, 11 figures and 3 tables) + supplementary
material (12 pages, 10 figures and 1 table). Accepted for publication in
Journal of Theoretical Biology on 27th April 201
A non-standard numerical scheme for an age-of-infection epidemic model
We propose a numerical method for approximating integro-differential
equations arising in age-of-infection epidemic models. The method is based on a
non-standard finite differences approximation of the integral term appearing in
the equation. The study of convergence properties and the analysis of the
qualitative behavior of the numerical solution show that it preserves all the
basic properties of the continuous model with no restrictive conditions on the
step-length of integration and that it recovers the continuous dynamic as
tends to zero.Comment: 17 pages, 3 figure
Layer-switching cost and optimality in information spreading on multiplex networks
We study a model of information spreading on multiplex networks, in which
agents interact through multiple interaction channels (layers), say online vs.\
offline communication layers, subject to layer-switching cost for transmissions
across different interaction layers. The model is characterized by the
layer-wise path-dependent transmissibility over a contact, that is dynamically
determined dependently on both incoming and outgoing transmission layers. We
formulate an analytical framework to deal with such path-dependent
transmissibility and demonstrate the nontrivial interplay between the
multiplexity and spreading dynamics, including optimality. It is shown that the
epidemic threshold and prevalence respond to the layer-switching cost
non-monotonically and that the optimal conditions can change in abrupt
non-analytic ways, depending also on the densities of network layers and the
type of seed infections. Our results elucidate the essential role of
multiplexity that its explicit consideration should be crucial for realistic
modeling and prediction of spreading phenomena on multiplex social networks in
an era of ever-diversifying social interaction layers.Comment: 15 pages, 7 figure
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