6,498 research outputs found
Effects of Contact Network Models on Stochastic Epidemic Simulations
The importance of modeling the spread of epidemics through a population has
led to the development of mathematical models for infectious disease
propagation. A number of empirical studies have collected and analyzed data on
contacts between individuals using a variety of sensors. Typically one uses
such data to fit a probabilistic model of network contacts over which a disease
may propagate. In this paper, we investigate the effects of different contact
network models with varying levels of complexity on the outcomes of simulated
epidemics using a stochastic Susceptible-Infectious-Recovered (SIR) model. We
evaluate these network models on six datasets of contacts between people in a
variety of settings. Our results demonstrate that the choice of network model
can have a significant effect on how closely the outcomes of an epidemic
simulation on a simulated network match the outcomes on the actual network
constructed from the sensor data. In particular, preserving degrees of nodes
appears to be much more important than preserving cluster structure for
accurate epidemic simulations.Comment: To appear at International Conference on Social Informatics (SocInfo)
201
Consistent approximation of epidemic dynamics on degree-heterogeneous clustered networks
Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To understand the joint effects of these two network properties on epidemic dynamics, the effective degree model of Lindquist et al. [28] is reformulated with a new moment closure to apply to highly clustered networks. A simulation study comparing alternative ODE models and stochastic simulations is performed for SIR (Susceptible–Infected–Removed) epidemic dynamics, including a test for the conjectured error behaviour in [40], providing evidence that this novel model can be a more accurate approximation to epidemic dynamics on complex networks than existing approaches
Mean-field-like approximations for stochastic processes on weighted and dynamic networks
The explicit use of networks in modelling stochastic processes such as epidemic dynamics
has revolutionised research into understanding the impact of contact pattern
properties, such as degree heterogeneity, preferential mixing, clustering, weighted and
dynamic linkages, on how epidemics invade, spread and how to best control them. In
this thesis, I worked on mean-field approximations of stochastic processes on networks
with particular focus on weighted and dynamic networks. I mostly used low dimensional
ordinary differential equation (ODE) models and explicit network-based stochastic simulations to model and analyse how epidemics become established and spread in weighted and dynamic networks.
I begin with a paper presenting the susceptible-infected-susceptible/recovered (SIS,
SIR) epidemic models on static weighted networks with different link weight distributions.
This work extends the pairwise model paradigm to weighted networks and gives
excellent agreement with simulations. The basic reproductive ratio, R0, is formulated
for SIR dynamics. The effects of link weight distribution on R0 and on the spread of
the disease are investigated in detail. This work is followed by a second paper, which
considers weighted networks in which the nodal degree and weights are not independent.
Moreover, two approximate models are explored: (i) the pairwise model and (ii)
the edge-based compartmental model. These are used to derive important epidemic
descriptors, including early growth rate, final epidemic size, basic reproductive ratio
and epidemic dynamics. Whilst the first two papers concentrate on static networks,
the third paper focuses on dynamic networks, where links can be activated and/or
deleted and this process can evolve together with the epidemic dynamics. We consider
an adaptive network with a link rewiring process constrained by spatial proximity. This
model couples SIS dynamics with that of the network and it investigates the impact of rewiring on the network structure and disease die-out induced by the rewiring process.
The fourth paper shows that the generalised master equations approach works well for
networks with low degree heterogeneity but it fails to capture networks with modest
or high degree heterogeneity. In particular, we show that a recently proposed generalisation
performs poorly, except for networks with low heterogeneity and high average
degree
A motif-based approach to network epidemics
Networks have become an indispensable tool in modelling infectious diseases, with the structure of epidemiologically relevant contacts known to affect both the dynamics of the infection process and the efficacy of intervention strategies. One of the key reasons for this is the presence of clustering in contact networks, which is typically analysed in terms of prevalence of triangles in the network. We present a more general approach, based on the prevalence of different four-motifs, in the context of ODE approximations to network dynamics. This is shown to outperform existing models for a range of small world networks
Dynamics of multi-stage infections on networks
This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider
Statistical inference framework for source detection of contagion processes on arbitrary network structures
In this paper we introduce a statistical inference framework for estimating
the contagion source from a partially observed contagion spreading process on
an arbitrary network structure. The framework is based on a maximum likelihood
estimation of a partial epidemic realization and involves large scale
simulation of contagion spreading processes from the set of potential source
locations. We present a number of different likelihood estimators that are used
to determine the conditional probabilities associated to observing partial
epidemic realization with particular source location candidates. This
statistical inference framework is also applicable for arbitrary compartment
contagion spreading processes on networks. We compare estimation accuracy of
these approaches in a number of computational experiments performed with the
SIR (susceptible-infected-recovered), SI (susceptible-infected) and ISS
(ignorant-spreading-stifler) contagion spreading models on synthetic and
real-world complex networks
A network epidemic model with preventive rewiring: comparative analysis of the initial phase
This paper is concerned with stochastic SIR and SEIR epidemic models on
random networks in which individuals may rewire away from infected neighbors at
some rate (and reconnect to non-infectious individuals with
probability or else simply drop the edge if ), so-called
preventive rewiring. The models are denoted SIR- and SEIR-, and
we focus attention on the early stages of an outbreak, where we derive
expression for the basic reproduction number and the expected degree of
the infectious nodes using two different approximation approaches. The
first approach approximates the early spread of an epidemic by a branching
process, whereas the second one uses pair approximation. The expressions are
compared with the corresponding empirical means obtained from stochastic
simulations of SIR- and SEIR- epidemics on Poisson and
scale-free networks. Without rewiring of exposed nodes, the two approaches
predict the same epidemic threshold and the same for both types of
epidemics, the latter being very close to the mean degree obtained from
simulated epidemics over Poisson networks. Above the epidemic threshold,
pairwise models overestimate the value of computed from simulations,
which turns out to be very close to the one predicted by the branching process
approximation. When exposed individuals also rewire with (perhaps
unaware of being infected), the two approaches give different epidemic
thresholds, with the branching process approximation being more in agreement
with simulations.Comment: 25 pages, 7 figure
Stochastic oscillations of adaptive networks: application to epidemic modelling
Adaptive-network models are typically studied using deterministic
differential equations which approximately describe their dynamics. In
simulations, however, the discrete nature of the network gives rise to
intrinsic noise which can radically alter the system's behaviour. In this
article we develop a method to predict the effects of stochasticity in adaptive
networks by making use of a pair-based proxy model. The technique is developed
in the context of an epidemiological model of a disease spreading over an
adaptive network of infectious contact. Our analysis reveals that in this model
the structure of the network exhibits stochastic oscillations in response to
fluctuations in the disease dynamic.Comment: 11 pages, 4 figure
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