arXiv subjects

P. A. Macri

Publications and source records attributed to P. A. Macri.

16 recordsLinked to original sources

arXiv2014

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.

physics.soc-ph↗

arXiv2014

Triple point induced by targeted autonomization on interdependent scale free networks

Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$ of nodes in one network, exposes the system to cascade of failures and, as a consequence, to a full collapse of the overall system. Therefore it is important to develop efficient strategies to avoid the collapse by increasing the robustness of the individual networks against failures. Here, we provide an exact theoretical approach to study the evolution of the cascade of failures on interdependent networks when a fraction $α$ of the nodes with higher connectivity in each individual network are autonomous. With this pattern of interdependency we found, for pair of heterogeneous networks, two critical percolation thresholds that depend on $α$, separating three regimes with very different network's final sizes that converge into a triple point in the plane $p-α$. Our findings suggest that the heterogeneity of the networks represented by high degree nodes is the responsible of the rich phase diagrams found in this and other investigations.

physics.soc-ph↗

arXiv2013

Triple Point in Correlated Interdependent Networks

Many real-world networks depend on other networks, often in non-trivial ways, to maintain their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction $1-p$ of nodes in one network randomly fails, the damage propagates to nodes in networks that are interdependent and a dynamic failure cascade occurs that affects the entire system. We present dynamic equations for two interdependent networks that allow us to reproduce the failure cascade for an arbitrary pattern of interdependency. We study the "rich club" effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction $α$ of the higher degree nodes on each network. We find a rich phase diagram in the plane $p-α$, with a triple point reminiscent of the triple point of liquids that separates a non-functional phase from two functional phases.

physics.soc-ph↗

arXiv2013

Slow epidemic extinction in populations with heterogeneous infection rates

We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is endowed with an infection rate $β_{ij} = λw_{ij}$ proportional to the intensity of their contact $w_{ij}$, with a distribution $P(w_{ij})$ taken from face-to-face experiments analyzed in Cattuto $et\;al.$ (PLoS ONE 5, e11596, 2010). We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter $λ$. Using a distribution of width $a$ we identify two large regions in the $a-λ$ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemic alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small $a$) and strong (large $a$) disorder, respectively.

physics.soc-ph↗

arXiv2013

Social distancing strategies against disease spreading

The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, $i.e$, the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, $i.e$, the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.

physics.soc-ph↗

arXiv2013

Temporal percolation of a susceptible adaptive network

In the last decades, many authors have used the susceptible-infected-recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the susceptible individuals. In this paper, we study the dynamic of the susceptible-infected-recovered model in an adaptive network that mimics the transitory deactivation of permanent social contacts, such as friendship and work-ship ties. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations for the fraction susceptible individuals in the susceptible biggest component. In particular, we focus on how the individual's behavior impacts on the dilution of the susceptible network. We show that, as a consequence, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time at which the giant susceptible component is destroyed. Our theoretical results are fully supported by extensive simulations.

physics.soc-ph↗

arXiv2013

Study of a Market Model with Conservative Exchanges on Complex Networks

Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum wealth or poverty line. On the other hand, the wealth distribution exhibited an exponential shape as a function of the square of the wealth. These results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme. In the present paper we study the effect of distributing the agents on a complex network. We have considered archetypical complex networks: Erdös-Rényi random networks and scale-free networks. The presence of a poverty line with finite wealth is preserved but spatial correlations are important, particularly between the degree of the node and the wealth. We present a detailed study of the correlations, as well as the changes in the Gini coefficient, that measures the inequality, as a function of the type and average degree of the considered networks.

physics.soc-ph↗

arXiv2012

Crossover from weak to strong disorder regime in the duration of epidemics

We study the Susceptible-Infected-Recovered model in complex networks, considering that not all individuals in the population interact in the same way between them. This heterogeneity between contacts is modeled by a continuous disorder. In our model the disorder represents the contact time or the closeness between individuals. We find that the duration time of an epidemic has a crossover with the system size, from a power law regime to a logarithmic regime depending on the transmissibility related to the strength of the disorder. Using percolation theory, we find that the duration of the epidemic scales as the average length of the branches of the infection. Our theoretical findings, supported by simulations, explains the crossover between the two regimes.

physics.soc-ph↗

arXiv2012

Temporal percolation of the susceptible network in an epidemic spreading

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity $Φ_S(t)$, namely, the probability that a given neighbor of a node is susceptible at time $t$, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time $t_c$ above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time $t_c$. Our theoretical results are confirmed by extensive simulations of the SIR process.

physics.soc-ph↗

arXiv2012

Intermittent social distancing strategy for epidemic control

We study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks. We characterize the effect of our strategy in the framework of the susceptible-infected-recovered model. In our model, based on local information, a susceptible individual interrupts the contact with an infected individual with a probability $σ$ and restores it after a fixed time $t_{b}$. We find that, depending on the network topology, in our social distancing strategy there exists a cutoff threshold $σ_{c}$ beyond which the epidemic phase disappears. Our results are supported by a theoretical framework and extensive simulations of the model. Furthermore we show that this strategy is very efficient because it leads to a "susceptible herd behavior" that protects a large fraction of susceptibles individuals. We explain our results using percolation arguments.

physics.soc-ph↗

arXiv2011

Effect of degree correlations above the first shell on the percolation transition

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on processes on top of them, has not yet been discussed. In this letter, using different correlation algorithms to generate assortative networks, we show that for very assortative networks the behavior of the main observables in percolation processes depends on the algorithm used to build the network. The different alghoritms used here introduce different inner structures that are missed in Pearson's coefficient. We explain the different behaviors through a generalization of Pearson's coefficient that allows to study the correlations at chemical distances l from a root node. We apply our findings to real networks.

physics.soc-ph↗

arXiv2010

Quarantine generated phase transition in epidemic spreading

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w_c separating a phase (w = w_c) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that w_c increases with the mean degree and heterogeneity of the network. We also find that w_c is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.

physics.soc-ph↗

arXiv2008

Effects of epidemic threshold definition on disease spread statistics

We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s_c. Using percolation theory to calculate the average fractional size of an epidemic, we find that the strength of the spanning link percolation cluster $P_{\infty}$ is an upper bound to . For small values of s_c, $P_{\infty}$ is no longer a good approximation, and the average fractional size has to be computed directly. The value of s_c for which $P_{\infty}$ is a good approximation is found to depend on the transmissibility T of the SIR. We also study Q, the probability that an SIR propagation reaches the epidemic mass s_c, and find that it is well characterized by percolation theory. We apply our results to real networks (DIMES and Tracerouter) to measure the consequences of the choice s_c on predictions of average outcome sizes of computer failure epidemics.

q-bio.PE↗

arXiv2008

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $ P(k) \sim k^{-λ}$ for $λ<3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $λ<3$.

cond-mat.stat-mech↗

arXiv2008

Using relaxational dynamics to reduce network congestion

We study the effects of relaxational dynamics on congestion pressure in scale free networks by analyzing the properties of the corresponding gradient networks (Z. Toroczkai, K. E. Bassler, Nature {\bf 428}, 716 (2004)). Using the Family model (F. Family, J. Phys. A, {\bf 19}, L441 (1986)) from surface-growth physics as single-step load-balancing dynamics, we show that the congestion pressure considerably drops on scale-free networks when compared with the same dynamics on random graphs. This is due to a structural transition of the corresponding gradient network clusters, which self-organize such as to reduce the congestion pressure. This reduction is enhanced when lowering the value of the connectivity exponent $λ$ towards 2.

cond-mat.stat-mech↗

arXiv2007

Discrete surface growth process as a synchronization mechanism for scale free complex networks

We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A {\bf 19} L441, (1986).] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-λ}$, where $k$ is the degree of a node and $λ$ his broadness, and compare it with the usually applied Edward-Wilkinson process [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London Ser. A {\bf 381},17 (1982) ]. In spite of both processes belong to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents $λ<3$ this is not true. Moreover, we show that for these ubiquitous cases the Edward-Wilkinson process enhances spontaneously the synchronization when the system size is increased, which is a non-physical result. Contrarily, the discrete surface growth process do not present this flaw and is applicable for every $λ$.

cond-mat.stat-mech↗