A message-passing approach to epidemic tracing and mitigation with apps

(5 pages,4 figures +SM)(5 pages,4 figures +SM)With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message--passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic

Numerical assessment of the percolation threshold using complement networks

Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however cause a deviation between the empirical percolation threshold pc and its model-predicted value πc. Here we show the existence of an empirical linear relation between pc and πc across a large number of real and model networks. Such a putatively universal relation can then be used to correct the estimated value of πc. We further show how to obtain a more precise relation using the concept of the complement graph, by investigating on the connection between the percolation threshold of a network, pc, and that of its complement, pc

Fragility and anomalous susceptibility of weakly interacting networks

Percolation is a fundamental concept that has brought new understanding of the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much fewer interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transitions are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer and has a well-defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers and is characterized by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous behavior of the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon, using a susceptibility measure that defines the range where the abrupt transition is more likely to occur. Finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition

Numerical Assessment of the Percolation Threshold Using Complement Networks

Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however cause a deviation between the empirical percolation threshold p_c and its model-predicted value q_c. Here we show the existence of an empirical linear relation between p_c and q_c across a large number of real and model networks. Such a putatively universal relation can then be used to correct the estimated value of q_c. We further show how to obtain a more precise relation using the concept of the complement graph, by investigating on the connection between the percolation threshold of a network and that of its complement

Fragility and anomalous susceptibility of weakly interacting networks

Percolation is a fundamental concept that has brought new understanding of the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much fewer interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transitions are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer and has a well-defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers and is characterized by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous behavior of the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon, using a susceptibility measure that defines the range where the abrupt transition is more likely to occur. Finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition

Multiple structural transitions in interacting networks

Many real-world systems can be modeled as interconnected multilayer networks, namely, a set of networks interacting with each other. Here, we present a perturbative approach to study the properties of a general class of interconnected networks as internetwork interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore, we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked systems, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems

Multiple structural transitions in interacting networks

Many real-world systems can be modeled as interconnected multilayer networks, namely, a set of networks interacting with each other. Here, we present a perturbative approach to study the properties of a general class of interconnected networks as internetwork interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore, we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked systems, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems

The mother-child attachment bond before and after birth: The role of maternal perception of traumatic childbirth

The quality of the mother-child attachment bond is a relevant factor for the psychosocial well-being of a child. However, some variables could affect this relationship, such as a perceived traumatic childbirth experience. The aim of this study was to explore the mediating role of the childbirth experience on the relationship between prenatal and postnatal attachment. A predictive study was conducted on 105 pregnant women aged 26 to 44 years. The data was collected at two different times: at week 31–32 of gestation (T1) and three months after childbirth (T2). The quality of maternal prenatal attachment has a significant and direct effect on postnatal mother-child attachment. Moreover, the quality of prenatal attachment represents a protective factor for the quality of childbirth experience, promoting a higher quality of postnatal attachment bond. Our results highlight the importance of supporting women throughout the perinatal period, starting from pregnancy to after childbirth