15 research outputs found
Effect of Coupling on the Epidemic Threshold in Interconnected Complex Networks: A Spectral Analysis
In epidemic modeling, the term infection strength indicates the ratio of
infection rate and cure rate. If the infection strength is higher than a
certain threshold -- which we define as the epidemic threshold - then the
epidemic spreads through the population and persists in the long run. For a
single generic graph representing the contact network of the population under
consideration, the epidemic threshold turns out to be equal to the inverse of
the spectral radius of the contact graph. However, in a real world scenario it
is not possible to isolate a population completely: there is always some
interconnection with another network, which partially overlaps with the contact
network. Results for epidemic threshold in interconnected networks are limited
to homogeneous mixing populations and degree distribution arguments. In this
paper, we adopt a spectral approach. We show how the epidemic threshold in a
given network changes as a result of being coupled with another network with
fixed infection strength. In our model, the contact network and the
interconnections are generic. Using bifurcation theory and algebraic graph
theory, we rigorously derive the epidemic threshold in interconnected networks.
These results have implications for the broad field of epidemic modeling and
control. Our analytical results are supported by numerical simulations.Comment: 7 page
Analysis of an epidemic model with awareness decay on regular random networks
The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness decay, through bifurcation analysis. By means of an equivalent mean-field model defined on regular random networks, we interpret the dynamics of the system in this region and prove that the existence of bifurcation for of this second epidemic threshold crucially depends on the absence of awareness decay. We show that the continuum of equilibria that characterizes the slow die-out dynamics collapses into a unique equilibrium when a constant rate of awareness decay is assumed, no matter how small, and that the resulting bifurcation from the disease-free equilibrium is equivalent to that of standard epidemic models. We illustrate these findings with continuous-time stochastic simulations on regular random networks with different degrees. Finally, the behaviour of solutions with and without decay in awareness is compared around the second epidemic threshold for a small rate of awareness decay
Optimal curing policy for epidemic spreading over a community network with heterogeneous population
The design of an efficient curing policy, able to stem an epidemic process at
an affordable cost, has to account for the structure of the population contact
network supporting the contagious process. Thus, we tackle the problem of
allocating recovery resources among the population, at the lowest cost possible
to prevent the epidemic from persisting indefinitely in the network.
Specifically, we analyze a susceptible-infected-susceptible epidemic process
spreading over a weighted graph, by means of a first-order mean-field
approximation. First, we describe the influence of the contact network on the
dynamics of the epidemics among a heterogeneous population, that is possibly
divided into communities. For the case of a community network, our
investigation relies on the graph-theoretical notion of equitable partition; we
show that the epidemic threshold, a key measure of the network robustness
against epidemic spreading, can be determined using a lower-dimensional
dynamical system. Exploiting the computation of the epidemic threshold, we
determine a cost-optimal curing policy by solving a convex minimization
problem, which possesses a reduced dimension in the case of a community
network. Lastly, we consider a two-level optimal curing problem, for which an
algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network
Spreading processes in Multilayer Networks
Several systems can be modeled as sets of interconnected networks or networks
with multiple types of connections, here generally called multilayer networks.
Spreading processes such as information propagation among users of an online
social networks, or the diffusion of pathogens among individuals through their
contact network, are fundamental phenomena occurring in these networks.
However, while information diffusion in single networks has received
considerable attention from various disciplines for over a decade, spreading
processes in multilayer networks is still a young research area presenting many
challenging research issues. In this paper we review the main models, results
and applications of multilayer spreading processes and discuss some promising
research directions.Comment: 21 pages, 3 figures, 4 table
Dynamical interaction between information and disease spreading in populations of moving agents
Copyright © 2018 Tech Science Press. Considering dynamical disease spreading network consisting of moving individuals, a new double-layer network is constructed, one where the information dissemination process takes place and the other where the dynamics of disease spreading evolves. On the basis of Markov chains theory, a new model characterizing the coupled dynamics between information dissemination and disease spreading in populations of moving agents is established and corresponding state probability equations are formulated to describe the probability in each state of every node at each moment. Monte Carlo simulations are performed to characterize the interaction process between information and disease spreading and investigate factors that influence spreading dynamics. Simulation results show that the increasing of information transmission rate can reduce the scale of disease spreading in some degree. Shortening infection period and strengthening consciousness for self-protection by decreasing individual’s scope of activity both can effectively reduce the final refractory density for the disease but have less effect on the information dissemination. In addition, the increasing of vaccination rate or decreasing of long-range travel can also reduce the scale of disease spreading
Network-centric interventions to contain the Syphilis epidemic in San Francisco
Altres ajuts: MPCUdG2016/047 de la Universitat de GironaThe number of reported early syphilis cases in San Francisco has increased steadily since 2005. It is not yet clear what factors are responsible for such an increase. A recent analysis of the sexual contact network of men who have sex with men with syphilis in San Francisco has discovered a large connected component, members of which have a significantly higher chance of syphilis and HIV compared to non-member individuals. This study investigates whether it is possible to exploit the existence of the largest connected component to design new notification strategies that can potentially contribute to reducing the number of cases. We develop a model capable of incorporating multiple types of notification strategies and compare the corresponding incidence of syphilis. Through extensive simulations, we show that notifying the community of the infection state of few central nodes appears to be the most effective approach, balancing the cost of notification and the reduction of syphilis incidence. Additionally, among the different measures of centrality, the eigenvector centrality reveals to be the best to reduce the incidence in the long term as long as the number of missing links (non-disclosed contacts) is not very large
The impact of the network topology on the viral prevalence: a node-based approach
This paper addresses the impact of the structure of the viral propagation network on the viral prevalence. For that purpose, a new epidemic model of computer virus, known as the node-based SLBS model, is proposed. Our analysis shows that the maximum eigenvalue of the underlying network is a key factor determining the viral prevalence. Specifically, the value range of the maximum eigenvalue is partitioned into three subintervals: viruses tend to extinction very quickly or approach extinction or persist depending on into which subinterval the maximum eigenvalue of the propagation network falls. Consequently, computer virus can be contained by adjusting the propagation network so that its maximum eigenvalue falls into the desired subinterval