3,949 research outputs found
Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies
The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August—which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015.H.E.S. thanks the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. L.D.V. and L.A.B. wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio
Predicting epidemic evolution on contact networks from partial observations
The massive employment of computational models in network epidemiology calls
for the development of improved inference methods for epidemic forecast. For
simple compartment models, such as the Susceptible-Infected-Recovered model,
Belief Propagation was proved to be a reliable and efficient method to identify
the origin of an observed epidemics. Here we show that the same method can be
applied to predict the future evolution of an epidemic outbreak from partial
observations at the early stage of the dynamics. The results obtained using
Belief Propagation are compared with Monte Carlo direct sampling in the case of
SIR model on random (regular and power-law) graphs for different observation
methods and on an example of real-world contact network. Belief Propagation
gives in general a better prediction that direct sampling, although the quality
of the prediction depends on the quantity under study (e.g. marginals of
individual states, epidemic size, extinction-time distribution) and on the
actual number of observed nodes that are infected before the observation time
Human mobility networks and persistence of rapidly mutating pathogens
Rapidly mutating pathogens may be able to persist in the population and reach
an endemic equilibrium by escaping hosts' acquired immunity. For such diseases,
multiple biological, environmental and population-level mechanisms determine
the dynamics of the outbreak, including pathogen's epidemiological traits (e.g.
transmissibility, infectious period and duration of immunity), seasonality,
interaction with other circulating strains and hosts' mixing and spatial
fragmentation. Here, we study a susceptible-infected-recovered-susceptible
model on a metapopulation where individuals are distributed in subpopulations
connected via a network of mobility flows. Through extensive numerical
simulations, we explore the phase space of pathogen's persistence and map the
dynamical regimes of the pathogen following emergence. Our results show that
spatial fragmentation and mobility play a key role in the persistence of the
disease whose maximum is reached at intermediate mobility values. We describe
the occurrence of different phenomena including local extinction and emergence
of epidemic waves, and assess the conditions for large scale spreading.
Findings are highlighted in reference to previous works and to real scenarios.
Our work uncovers the crucial role of hosts' mobility on the ecological
dynamics of rapidly mutating pathogens, opening the path for further studies on
disease ecology in the presence of a complex and heterogeneous environment.Comment: 29 pages, 7 figures. Submitted for publicatio
Fluctuating epidemics on adaptive networks
A model for epidemics on an adaptive network is considered. Nodes follow an
SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are
rewired to break links from non-infected nodes to infected nodes and are
reformed to connect to other non-infected nodes, as the nodes that are not
infected try to avoid the infection. Monte Carlo simulation and numerical
solution of a mean field model are employed. The introduction of rewiring
affects both the network structure and the epidemic dynamics. Degree
distributions are altered, and the average distance from a node to the nearest
infective increases. The rewiring leads to regions of bistability where either
an endemic or a disease-free steady state can exist. Fluctuations around the
endemic state and the lifetime of the endemic state are considered. The
fluctuations are found to exhibit power law behavior.Comment: Submitted to Phys Rev
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
Shadows of the SIS immortality transition in small networks
Much of the research on the behavior of the SIS model on networks has
concerned the infinite size limit; in particular the phase transition between a
state where outbreaks can reach a finite fraction of the population, and a
state where only a finite number would be infected. For finite networks, there
is also a dynamic transition---the immortality transition---when the
per-contact transmission probability reaches one. If ,
the probability that an outbreak will survive by an observation time tends
to zero as ; if , this probability is one.
We show that treating as a critical point predicts the
-dependence of the survival probability also for more moderate
-values. The exponent, however, depends on the underlying network.
This fact could, by measuring how a vertex' deletion changes the exponent, be
used to evaluate the role of a vertex in the outbreak. Our work also confirms
an extremely clear separation between the early die-off (from the outbreak
failing to take hold in the population) and the later extinctions
(corresponding to rare stochastic events of several consecutive transmission
events failing to occur).Comment: Bug fixes from the first versio
Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies
The Ebola virus is spreading throughout West Africa and is causing thousands
of deaths. In order to quantify the effectiveness of different strategies for
controlling the spread, we develop a mathematical model in which the
propagation of the Ebola virus through Liberia is caused by travel between
counties. For the initial months in which the Ebola virus spreads, we find that
the arrival times of the disease into the counties predicted by our model are
compatible with World Health Organization data, but we also find that reducing
mobility is insufficient to contain the epidemic because it delays the arrival
of Ebola virus in each county by only a few weeks. We study the effect of a
strategy in which safe burials are increased and effective hospitalisation
instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii)
one in mid-August---which was the actual time that strong interventions began
in Liberia. We find that if scenario (i) had been pursued the lifetime of the
epidemic would have been three months shorter and the total number of infected
individuals 80\% less than in scenario (ii). Our projection under scenario (ii)
is that the spreading will stop by mid-spring 2015
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