2,008 research outputs found
A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks
A better characterization of the early growth dynamics of an epidemic is
needed to dissect the important drivers of disease transmission. We introduce a
2-parameter generalized-growth model to characterize the ascending phase of an
outbreak and capture epidemic profiles ranging from sub-exponential to
exponential growth. We test the model against empirical outbreak data
representing a variety of viral pathogens and provide simulations highlighting
the importance of sub-exponential growth for forecasting purposes. We applied
the generalized-growth model to 20 infectious disease outbreaks representing a
range of transmission routes. We uncovered epidemic profiles ranging from very
slow growth (p=0.14 for the Ebola outbreak in Bomi, Liberia (2014)) to near
exponential (p>0.9 for the smallpox outbreak in Khulna (1972), and the 1918
pandemic influenza in San Francisco). The foot-and-mouth disease outbreak in
Uruguay displayed a profile of slower growth while the growth pattern of the
HIV/AIDS epidemic in Japan was approximately linear. The West African Ebola
epidemic provided a unique opportunity to explore how growth profiles vary by
geography; analysis of the largest district-level outbreaks revealed
substantial growth variations (mean p=0.59, range: 0.14-0.97). Our findings
reveal significant variation in epidemic growth patterns across different
infectious disease outbreaks and highlights that sub-exponential growth is a
common phenomenon. Sub-exponential growth profiles may result from
heterogeneity in contact structures or risk groups, reactive behavior changes,
or the early onset of interventions strategies, and consideration of
"deceleration parameters" may be useful to refine existing mathematical
transmission models and improve disease forecasts.Comment: 31 pages, 9 Figures, 1 Supp. Figure, 1 Table, final accepted version
(in press), Epidemics - The Journal on Infectious Disease Dynamics, 201
Early warning signs for saddle-escape transitions in complex networks
Many real world systems are at risk of undergoing critical transitions,
leading to sudden qualitative and sometimes irreversible regime shifts. The
development of early warning signals is recognized as a major challenge. Recent
progress builds on a mathematical framework in which a real-world system is
described by a low-dimensional equation system with a small number of key
variables, where the critical transition often corresponds to a bifurcation.
Here we show that in high-dimensional systems, containing many variables, we
frequently encounter an additional non-bifurcative saddle-type mechanism
leading to critical transitions. This generic class of transitions has been
missed in the search for early-warnings up to now. In fact, the saddle-type
mechanism also applies to low-dimensional systems with saddle-dynamics. Near a
saddle a system moves slowly and the state may be perceived as stable over
substantial time periods. We develop an early warning sign for the saddle-type
transition. We illustrate our results in two network models and epidemiological
data. This work thus establishes a connection from critical transitions to
networks and an early warning sign for a new type of critical transition. In
complex models and big data we anticipate that saddle-transitions will be
encountered frequently in the future.Comment: revised versio
Local vs. long-range infection in unidimensional epidemics
We study the effects of local and distance interactions in the unidimensional
contact process (CP). In the model, each site of a lattice is occupied by an
individual, which can be healthy or infected. As in the standard CP, each
infected individual spreads the disease to one of its first-neighbors with rate
, and with unitary rate, it becomes healthy. However, in our model, an
infected individual can transmit the disease to an individual at a distance
apart. This step mimics a vector-mediated transmission. We observe the
host-host interactions do not alter the critical exponents significantly in
comparison to a process with only L\'evy-type interactions. Our results
confirm, numerically, early field-theoretic predictions.Comment: 8 pages, 6 figures, to appear on Frontiers in Physic
Epidemiological models with parametric heterogeneity: Deterministic theory for closed populations
We present a unified mathematical approach to epidemiological models with
parametric heterogeneity, i.e., to the models that describe individuals in the
population as having specific parameter (trait) values that vary from one
individuals to another. This is a natural framework to model, e.g.,
heterogeneity in susceptibility or infectivity of individuals. We review, along
with the necessary theory, the results obtained using the discussed approach.
In particular, we formulate and analyze an SIR model with distributed
susceptibility and infectivity, showing that the epidemiological models for
closed populations are well suited to the suggested framework. A number of
known results from the literature is derived, including the final epidemic size
equation for an SIR model with distributed susceptibility. It is proved that
the bottom up approach of the theory of heterogeneous populations with
parametric heterogeneity allows to infer the population level description,
which was previously used without a firm mechanistic basis; in particular, the
power law transmission function is shown to be a consequence of the initial
gamma distributed susceptibility and infectivity. We discuss how the general
theory can be applied to the modeling goals to include the heterogeneous
contact population structure and provide analysis of an SI model with
heterogeneous contacts. We conclude with a number of open questions and
promising directions, where the theory of heterogeneous populations can lead to
important simplifications and generalizations.Comment: 26 pages, 6 figures, submitted to Mathematical Modelling of Natural
Phenomen
Differential equation and complex network approaches for epidemic modelling
This study consists of three parts. The first part focuses on bifurcation analysis of epidemic models with sub-optimal immunity and saturated treatment/recovery rate as well as nonlinear incidence rate. The second part of the research focuses on estimating the domain of attraction for sub-optimal immunity epidemic models. In the third part of the research, we develop a bond percolation model for community clustered networks with an arbitrarily specified joint degree distribution
Epicasting: An Ensemble Wavelet Neural Network (EWNet) for Forecasting Epidemics
Infectious diseases remain among the top contributors to human illness and
death worldwide, among which many diseases produce epidemic waves of infection.
The unavailability of specific drugs and ready-to-use vaccines to prevent most
of these epidemics makes the situation worse. These force public health
officials and policymakers to rely on early warning systems generated by
reliable and accurate forecasts of epidemics. Accurate forecasts of epidemics
can assist stakeholders in tailoring countermeasures, such as vaccination
campaigns, staff scheduling, and resource allocation, to the situation at hand,
which could translate to reductions in the impact of a disease. Unfortunately,
most of these past epidemics exhibit nonlinear and non-stationary
characteristics due to their spreading fluctuations based on seasonal-dependent
variability and the nature of these epidemics. We analyse a wide variety of
epidemic time series datasets using a maximal overlap discrete wavelet
transform (MODWT) based autoregressive neural network and call it EWNet model.
MODWT techniques effectively characterize non-stationary behavior and seasonal
dependencies in the epidemic time series and improve the nonlinear forecasting
scheme of the autoregressive neural network in the proposed ensemble wavelet
network framework. From a nonlinear time series viewpoint, we explore the
asymptotic stationarity of the proposed EWNet model to show the asymptotic
behavior of the associated Markov Chain. We also theoretically investigate the
effect of learning stability and the choice of hidden neurons in the proposal.
From a practical perspective, we compare our proposed EWNet framework with
several statistical, machine learning, and deep learning models. Experimental
results show that the proposed EWNet is highly competitive compared to the
state-of-the-art epidemic forecasting methods
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