200 research outputs found
Sudden spreading of infections in an epidemic model with a finite seed fraction
We study a simple case of the susceptible-weakened-infected-removed model in
regular random graphs in a situation where an epidemic starts from a finite
fraction of initially infected nodes (seeds). Previous studies have shown that,
assuming a single seed, this model exhibits a kind of discontinuous transition
at a certain value of infection rate. Performing Monte Carlo simulations and
evaluating approximate master equations, we find that the present model has two
critical infection rates for the case with a finite seed fraction. At the first
critical rate the system shows a percolation transition of clusters composed of
removed nodes, and at the second critical rate, which is larger than the first
one, a giant cluster suddenly grows and the order parameter jumps even though
it has been already rising. Numerical evaluation of the master equations shows
that such sudden epidemic spreading does occur if the degree of the underlying
network is large and the seed fraction is small.Comment: 9 page
Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks
This study focuses on investigating the manner in which a prompt quarantine
measure suppresses epidemics in networks. A simple and ideal quarantine measure
is considered in which an individual is detected with a probability immediately
after it becomes infected and the detected one and its neighbors are promptly
isolated. The efficiency of this quarantine in suppressing a
susceptible-infected-removed (SIR) model is tested in random graphs and
uncorrelated scale-free networks. Monte Carlo simulations are used to show that
the prompt quarantine measure outperforms random and acquaintance preventive
vaccination schemes in terms of reducing the number of infected individuals.
The epidemic threshold for the SIR model is analytically derived under the
quarantine measure, and the theoretical findings indicate that prompt
executions of quarantines are highly effective in containing epidemics. Even if
infected individuals are detected with a very low probability, the SIR model
under a prompt quarantine measure has finite epidemic thresholds in fat-tailed
scale-free networks in which an infected individual can always cause an
outbreak of a finite relative size without any measure. The numerical
simulations also demonstrate that the present quarantine measure is effective
in suppressing epidemics in real networks.Comment: 10 pages, 7 figure
Hierarchical scale-free network is fragile against random failure
We investigate site percolation in a hierarchical scale-free network known as
the Dorogovtsev- Goltsev-Mendes network. We use the generating function method
to show that the percolation threshold is 1, i.e., the system is not in the
percolating phase when the occupation probability is less than 1. The present
result is contrasted to bond percolation in the same network of which the
percolation threshold is zero. We also show that the percolation threshold of
intentional attacks is 1. Our results suggest that this hierarchical scale-free
network is very fragile against both random failure and intentional attacks.
Such a structural defect is common in many hierarchical network models.Comment: 11 pages, 4 figure
Critical Phase of Bond Percolations on Growing Networks
The critical phase of bond percolation on the random growing tree is
examined. It is shown that the root cluster grows with the system size as
and the mean number of clusters with size per node follows a power
function in the whole range of open bond probability
. The exponent and the fractal exponent are also derived as a
function of and the degree exponent , and are found to satisfy the
scaling relation . Numerical results with several network
sizes are quite well fitted by a finite size scaling for a wide range of
and , which gives a clear evidence for the existence of a critical
phase.Comment: 5 pages, 4 figures; accepted for publication in Physical Review
Robustness of correlated networks against propagating attacks
We investigate robustness of correlated networks against propagating attacks
modeled by a susceptible-infected-removed model. By Monte-Carlo simulations, we
numerically determine the first critical infection rate, above which a global
outbreak of disease occurs, and the second critical infection rate, above which
disease disintegrates the network. Our result shows that correlated networks
are robust compared to the uncorrelated ones, regardless of whether they are
assortative or disassortative, when a fraction of infected nodes in an initial
state is not too large. For large initial fraction, disassortative network
becomes fragile while assortative network holds robustness. This behavior is
related to the layered network structure inevitably generated by a rewiring
procedure we adopt to realize correlated networks.Comment: 6 pages, 13 figure
Profile and scaling of the fractal exponent of percolations in complex networks
We propose a novel finite size scaling analysis for percolation transition
observed in complex networks. While it is known that cooperative systems in
growing networks often undergo an infinite order transition with inverted
Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical
simulations to determine the transition point precisely. Since the neighbor of
the ordered phase is not a simple disordered phase but a critical phase,
conventional finite size scaling technique does not work. In our finite size
scaling, the forms of the scaling functions for the order parameter and the
fractal exponent determine the transition point and critical exponents
numerically for an infinite order transition as well as a standard second order
transition. We confirm the validity of our scaling hypothesis through
Monte-Carlo simulations for bond percolations in some network models: the
decorated (2,2)-flower and the random attachment growing network, where an
infinite order transition occurs, and the configuration model, where a second
order transition occurs.Comment: 6 page
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