8,707 research outputs found
Rich Dynamics of an Epidemic Model with Saturation Recovery
A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction number ℝ0 is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region
Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons
We study the dynamical states that emerge in a small-world network of
recurrently coupled excitable neurons through both numerical and analytical
methods. These dynamics depend in large part on the fraction of long-range
connections or `short-cuts' and the delay in the neuronal interactions.
Persistent activity arises for a small fraction of `short-cuts', while a
transition to failure occurs at a critical value of the `short-cut' density.
The persistent activity consists of multi-stable periodic attractors, the
number of which is at least on the order of the number of neurons in the
network. For long enough delays, network activity at high `short-cut' densities
is shown to exhibit exceedingly long chaotic transients whose failure-times
averaged over many network configurations follow a stretched exponential. We
show how this functional form arises in the ensemble-averaged activity if each
network realization has a characteristic failure-time which is exponentially
distributed.Comment: 14 pages 23 figure
Epidemic spreading on preferred degree adaptive networks
We study the standard SIS model of epidemic spreading on networks where
individuals have a fluctuating number of connections around a preferred degree
. Using very simple rules for forming such preferred degree networks,
we find some unusual statistical properties not found in familiar
Erd\H{o}s-R\'{e}nyi or scale free networks. By letting depend on the
fraction of infected individuals, we model the behavioral changes in response
to how the extent of the epidemic is perceived. In our models, the behavioral
adaptations can be either `blind' or `selective' -- depending on whether a node
adapts by cutting or adding links to randomly chosen partners or selectively,
based on the state of the partner. For a frozen preferred network, we find that
the infection threshold follows the heterogeneous mean field result
and the phase diagram matches the predictions of
the annealed adjacency matrix (AAM) approach. With `blind' adaptations,
although the epidemic threshold remains unchanged, the infection level is
substantially affected, depending on the details of the adaptation. The
`selective' adaptive SIS models are most interesting. Both the threshold and
the level of infection changes, controlled not only by how the adaptations are
implemented but also how often the nodes cut/add links (compared to the time
scales of the epidemic spreading). A simple mean field theory is presented for
the selective adaptations which capture the qualitative and some of the
quantitative features of the infection phase diagram.Comment: 21 pages, 7 figure
Anomalous Contagion and Renormalization in Dynamical Networks with Nodal Mobility
The common real-world feature of individuals migrating through a network --
either in real space or online -- significantly complicates understanding of
network processes. Here we show that even though a network may appear static on
average, underlying nodal mobility can dramatically distort outbreak profiles.
Highly nonlinear dynamical regimes emerge in which increasing mobility either
amplifies or suppresses outbreak severity. Predicted profiles mimic recent
outbreaks of real-space contagion (social unrest) and online contagion
(pro-ISIS support). We show that this nodal mobility can be renormalized in a
precise way for a particular class of dynamical networks
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