1,321 research outputs found
Dynamics of interacting diseases
Current modeling of infectious diseases allows for the study of complex and
realistic scenarios that go from the population to the individual level of
description. However, most epidemic models assume that the spreading process
takes place on a single level (be it a single population, a meta-population
system or a network of contacts). In particular, interdependent contagion
phenomena can only be addressed if we go beyond the scheme one pathogen-one
network. In this paper, we propose a framework that allows describing the
spreading dynamics of two concurrent diseases. Specifically, we characterize
analytically the epidemic thresholds of the two diseases for different
scenarios and also compute the temporal evolution characterizing the unfolding
dynamics. Results show that there are regions of the parameter space in which
the onset of a disease's outbreak is conditioned to the prevalence levels of
the other disease. Moreover, we show, for the SIS scheme, that under certain
circumstances, finite and not vanishing epidemic thresholds are found even at
the thermodynamic limit for scale-free networks. For the SIR scenario, the
phenomenology is richer and additional interdependencies show up. We also find
that the secondary thresholds for the SIS and SIR models are different, which
results directly from the interaction between both diseases. Our work thus
solve an important problem and pave the way towards a more comprehensive
description of the dynamics of interacting diseases.Comment: 24 pages, 9 figures, 4 tables, 3 appendices. Final version accepted
for publication in Physical Review
Information Spreading on Almost Torus Networks
Epidemic modeling has been extensively used in the last years in the field of
telecommunications and computer networks. We consider the popular
Susceptible-Infected-Susceptible spreading model as the metric for information
spreading. In this work, we analyze information spreading on a particular class
of networks denoted almost torus networks and over the lattice which can be
considered as the limit when the torus length goes to infinity. Almost torus
networks consist on the torus network topology where some nodes or edges have
been removed. We find explicit expressions for the characteristic polynomial of
these graphs and tight lower bounds for its computation. These expressions
allow us to estimate their spectral radius and thus how the information spreads
on these networks
Traffic Control for Network Protection Against Spreading Processes
Epidemic outbreaks in human populations are facilitated by the underlying
transportation network. We consider strategies for containing a viral spreading
process by optimally allocating a limited budget to three types of protection
resources: (i) Traffic control resources, (ii), preventative resources and
(iii) corrective resources. Traffic control resources are employed to impose
restrictions on the traffic flowing across directed edges in the transportation
network. Preventative resources are allocated to nodes to reduce the
probability of infection at that node (e.g. vaccines), and corrective resources
are allocated to nodes to increase the recovery rate at that node (e.g.
antidotes). We assume these resources have monetary costs associated with them,
from which we formalize an optimal budget allocation problem which maximizes
containment of the infection. We present a polynomial time solution to the
optimal budget allocation problem using Geometric Programming (GP) for an
arbitrary weighted and directed contact network and a large class of resource
cost functions. We illustrate our approach by designing optimal traffic control
strategies to contain an epidemic outbreak that propagates through a real-world
air transportation network.Comment: arXiv admin note: text overlap with arXiv:1309.627
- …