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<![CDATA[Dynamical correlations and pairwise theory for the symbiotic contact process on networks]]>
https://www.researchpad.co/article/elastic_article_8226
The twospecies symbiotic contact process (2SCP) is a stochastic process in which each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise meanfield theory. This approach is compared with the ordinary onesite theory and stochastic simulations. We show that our approach significantly outperforms the onesite theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise meanfield, even for relatively small values of vertex degree, where expressive deviations of the standard meanfield are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the onesite method. Our theoretical results are corroborated by extensive numerical simulations.
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<![CDATA[Role of structural holes in containing spreading processes]]>
https://www.researchpad.co/article/elastic_article_8224
Structural holes are channels or paths spanned by a group of indirectly connected nodes and their intermediary in a network. In this work we emphasize the interesting role of structural holes as brokers for information propagation. Based on the distribution of the structural hole numbers associated with each node, we propose a simple yet effective approach for choosing the most influential nodes to immunize in containing the spreading processes. Using a wide spectrum of large realworld networks, we demonstrate that the proposed approach outperforms conventional methods in a remarkable way. In particular, we find that the performance gains of our approach are particularly prominent for networks with high transitivity and assortativity, which verifies the vital role of structural holes in information diffusion on networked systems.
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<![CDATA[Backbone reconstruction in temporal networks from epidemic data]]>
https://www.researchpad.co/article/elastic_article_8222
Many complex systems are characterized by timevarying patterns of interactions. These interactions comprise strong ties, driven by dyadic relationships, and weak ties, based on nodespecific attributes. The interplay between strong and weak ties plays an important role on dynamical processes that could unfold on complex systems. However, seldom do we have access to precise information about the timevarying topology of interaction patterns. A particularly elusive question is to distinguish strong from weak ties, on the basis of the sole node dynamics. Building upon analytical results, we propose a statisticallyprincipled algorithm to reconstruct the backbone of strong ties from data of a spreading process, consisting of the time series of individuals' states. Our method is numerically validated over a range of synthetic datasets, encapsulating salient features of realworld systems. Motivated by compelling evidence, we propose the integration of our algorithm in a targeted immunization strategy that prioritizes influential nodes in the inferred backbone. Through Monte Carlo simulations on synthetic networks and a realworld case study, we demonstrate the viability of our approach.
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<![CDATA[Efficient spreadsize approximation of opinion spreading in general social networks]]>
https://www.researchpad.co/article/elastic_article_8219
In contemporary society, understanding how information, such as trends and viruses, spreads in various social networks is an important topic in many areas. However, it is difficult to mathematically measure how widespread the information is, especially for a general network structure. There have been studies on opinion spreading, but many studies are limited to specific spreading models such as the susceptibleinfectedrecovered model and the independent cascade model, and it is difficult to apply these studies to various situations. In this paper, we first suggest a general opinion spreading model (GOSM) that generalizes a large class of popular spreading models. In this model, each node has one of several states, and the state changes through interaction with neighboring nodes at discrete time intervals. Next, we show that many GOSMs have a stable property that is a GOSM version of a uniform equicontinuity. Then, we provide an approximation method to approximate the expected spread size for stable GOSMs. For the approximation method, we propose a concentration theorem that guarantees that a generalized meanfield theorem calculates the expected spreading size within small error bounds for finite time steps for a slightly dense network structure. Furthermore, we prove that a “single simulation” of running the Monte Carlo simulation is sufficient to approximate the expected spreading size. We conduct experiments on both synthetic and realworld networks and show that our generalized approximation method well predicts the state density of the various models, especially in graphs with a large number of nodes. Experimental results show that the generalized meanfield approximation and a single Monte Carlo simulation converge as shown in the concentration theorem.
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<![CDATA[Equivalence of several generalized percolation models on networks]]>
https://www.researchpad.co/article/elastic_article_8216
In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, kcore percolation, bootstrap percolation, the generalized epidemic process, and the Watts threshold model (WTM). We show that—except for bond percolation—each of these processes arises as a special case of the WTM, and bond percolation arises from a small modification. In fact “heterogeneous kcore percolation,” a corresponding “heterogeneous bootstrap percolation” model, and the generalized epidemic process are completely equivalent to one another and the WTM. We further show that a natural generalization of the WTM in which individuals “transmit” or “send a message” to their neighbors with some probability less than 1 can be reformulated in terms of the WTM, and so this apparent generalization is in fact not more general. Finally, we show that in bond percolation, finding the set of nodes in the component containing a given node is equivalent to finding the set of nodes activated if that node is initially activated and the node thresholds are chosen from the appropriate distribution. A consequence of these results is that mathematical techniques developed for the WTM apply to these other models as well, and techniques that were developed for some particular case may in fact apply much more generally.
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<![CDATA[Hysteresis loop of nonperiodic outbreaks of recurrent epidemics]]>
https://www.researchpad.co/article/elastic_article_8215
Most of the studies on epidemics so far have focused on the growing phase, such as how an epidemic spreads and what are the conditions for an epidemic to break out in a variety of cases. However, we discover from real data that on a large scale, the spread of an epidemic is in fact a recurrent event with distinctive growing and recovering phases, i.e., a hysteresis loop. We show here that the hysteresis loop can be reproduced in epidemic models provided that the infectious rate is adiabatically increased or decreased before the system reaches its stationary state. Two ways to the hysteresis loop are revealed, which is helpful in understanding the mechanics of infections in real evolution. Moreover, a theoretical analysis is presented to explain the mechanism of the hysteresis loop.
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<![CDATA[Discretetime dynamic network model for the spread of susceptibleinfectiverecovered diseases]]>
https://www.researchpad.co/article/elastic_article_8214
We propose a discretetime dynamic network model describing the spread of susceptibleinfectiverecovered diseases in a population. We consider the case in which the nodes in the network change their links due to social mixing dynamics as well as in response to the disease. The model shows the behavior that, as we increase social mixing, disease spread is inhibited in certain cases, while in other cases it is enhanced. We also extend this dynamic network model to take into account the case of hidden infection. Here we find that, as expected, the disease spreads more readily if there is a time period after contracting the disease during which an individual is infective but is not known to have the disease.
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<![CDATA[Epidemic spreading in random rectangular networks]]>
https://www.researchpad.co/article/elastic_article_8212
The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGGs) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain realworld scenarios—like in the analysis of a disease propagating through plants—the shape of the plots and fields where the host of the disease is located may play a fundamental role in the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots or fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph and we consider a lower bound for the epidemic threshold of a susceptibleinfectedsusceptible model or a susceptibleinfectedrecovered model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot or field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots or fields of the same area and different shapes.
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<![CDATA[Influence of trust in the spreading of information]]>
https://www.researchpad.co/article/elastic_article_8211
The understanding and prediction of information diffusion processes on networks is a major challenge in network theory with many implications in social sciences. Many theoretical advances occurred due to stochastic spreading models. Nevertheless, these stochastic models overlooked the influence of rational decisions on the outcome of the process. For instance, different levels of trust in acquaintances do play a role in information spreading, and actors may change their spreading decisions during the information diffusion process accordingly. Here, we study an informationspreading model in which the decision to transmit or not is based on trust. We explore the interplay between the propagation of information and the trust dynamics happening on a twolayer multiplex network. Actors' trustable or untrustable states are defined as accumulated cooperation or defection behaviors, respectively, in a Prisoner's Dilemma setup, and they are controlled by a memory span. The propagation of information is abstracted as a threshold model on the informationspreading layer, where the threshold depends on the trustability of agents. The analysis of the model is performed using a tree approximation and validated on homogeneous and heterogeneous networks. The results show that the memory of previous actions has a significant effect on the spreading of information. For example, the less memory that is considered, the higher is the diffusion. Information is highly promoted by the emergence of trustable acquaintances. These results provide insight into the effect of plausible biases on spreading dynamics in a multilevel networked system.
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<![CDATA[Efficiency of prompt quarantine measures on a susceptibleinfectedremoved model in networks]]>
https://www.researchpad.co/article/elastic_article_8209
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 susceptibleinfectedremoved (SIR) model is tested in random graphs and uncorrelated scalefree 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 fattailed scalefree 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.
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<![CDATA[Control of epidemics via social partnership adjustment]]>
https://www.researchpad.co/article/elastic_article_8208
Epidemic control is of great importance for human society. Adjusting interacting partners is an effective individualized control strategy. Intuitively, it is done either by shortening the interaction time between susceptible and infected individuals or by increasing the opportunities for contact between susceptible individuals. Here, we provide a comparative study on these two control strategies by establishing an epidemic model with nonuniform stochastic interactions. It seems that the two strategies should be similar, since shortening the interaction time between susceptible and infected individuals somehow increases the chances for contact between susceptible individuals. However, analytical results indicate that the effectiveness of the former strategy sensitively depends on the infectious intensity and the combinations of different interaction rates, whereas the latter one is quite robust and efficient. Simulations are shown to verify our analytical predictions. Our work may shed light on the strategic choice of disease control.
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<![CDATA[Effect of risk perception on epidemic spreading in temporal networks]]>
https://www.researchpad.co/article/elastic_article_8206
Many progresses in the understanding of epidemic spreading models have been obtained thanks to numerous modeling efforts and analytical and numerical studies, considering host populations with very different structures and properties, including complex and temporal interaction networks. Moreover, a number of recent studies have started to go beyond the assumption of an absence of coupling between the spread of a disease and the structure of the contacts on which it unfolds. Models including awareness of the spread have been proposed, to mimic possible precautionary measures taken by individuals that decrease their risk of infection, but have mostly considered static networks. Here, we adapt such a framework to the more realistic case of temporal networks of interactions between individuals. We study the resulting model by analytical and numerical means on both simple models of temporal networks and empirical timeresolved contact data. Analytical results show that the epidemic threshold is not affected by the awareness but that the prevalence can be significantly decreased. Numerical studies on synthetic temporal networks highlight, however, the presence of very strong finitesize effects, resulting in a significant shift of the effective epidemic threshold in the presence of risk awareness. For empirical contact networks, the awareness mechanism leads as well to a shift in the effective threshold and to a strong reduction of the epidemic prevalence.
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<![CDATA[Accurate ranking of influential spreaders in networks based on dynamically asymmetric link weights]]>
https://www.researchpad.co/article/elastic_article_8204
We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes i and j may differ in its importance for spreading from i to j and from j to i. The key issue is whether node j, after infected by i through the edge, would reach out to other nodes that i itself could not reach directly. It becomes necessary to invoke two unequal weights wij and wji characterizing the importance of an edge according to the neighborhoods of nodes i and j. The total asymmetric directional weights originating from a node leads to a novel measure si, which quantifies the impact of the node in spreading processes. An sshell decomposition scheme further assigns an sshell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on si and the weighted coreness are demonstrated by applying them to nine realworld networks. Results show that they generally outperform rankings based on the nodes' degree and kshell index while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.
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<![CDATA[Fundamental difference between superblockers and superspreaders in networks]]>
https://www.researchpad.co/article/elastic_article_8202
Two important problems regarding spreading phenomena in complex topologies are the optimal selection of node sets either to minimize or maximize the extent of outbreaks. Both problems are nontrivial when a small fraction of the nodes in the network can be used to achieve the desired goal. The minimization problem is equivalent to a structural optimization. The “superblockers,” i.e., the nodes that should be removed from the network to minimize the size of outbreaks, are those nodes that make connected components as small as possible. “Superspreaders” are instead the nodes such that, if chosen as initiators, they maximize the average size of outbreaks. The identity of superspreaders is expected to depend not just on the topology, but also on the specific dynamics considered. Recently, it has been conjectured that the two optimization problems might be equivalent, in the sense that superblockers act also as superspreaders. In spite of its potential groundbreaking importance, no empirical study has been performed to validate this conjecture. In this paper, we perform an extensive analysis over a large set of realworld networks to test the similarity between sets of superblockers and of superspreaders. We show that the two optimization problems are not equivalent: superblockers do not act as optimal spreaders.
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<![CDATA[Interplay between cost and benefits triggers nontrivial vaccination uptake]]>
https://www.researchpad.co/article/elastic_article_8197
The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total immunization is not guaranteed. Imperfect immunization has driven the emergence of antivaccine movements that totally alter the predictions about the epidemic incidence. Here, we propose a mathematically solvable meanfield vaccination model to mimic the spontaneous adoption of vaccines against influenzalike diseases and the expected epidemic incidence. The results are in agreement with extensive Monte Carlo simulations of the epidemics and vaccination coevolutionary processes. Interestingly, the results reveal a nonmonotonic behavior on the vaccination coverage that increases with the imperfection of the vaccine and after decreases. This apparent counterintuitive behavior is analyzed and understood from stability principles of the proposed mathematical model.
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<![CDATA[Bursting endemic bubbles in an adaptive network]]>
https://www.researchpad.co/article/elastic_article_8196
The spread of an infectious disease is known to change people's behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavioral change have found oscillations, but in an extremely narrow region of the parameter space, which contrasts with intuition and available data. In this paper we propose a simple susceptibleinfectedsusceptible epidemic model on an adaptive network with timedelayed rewiring, and show that oscillatory solutions are now present in a wide region of the parameter space. Altering the transmission or rewiring rates reveals the presence of an endemic bubble—an enclosed region of the parameter space where oscillations are observed.
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<![CDATA[Spontaneous repulsion in the A+B→0 reaction on coupled networks]]>
https://www.researchpad.co/article/elastic_article_8193
We study the transient dynamics of an A+B→0 process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions q of cross couplings, the concentration of A (or B) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time tx. By numerical and analytical arguments, we show that for symmetric and homogeneous structures tx∝(〈k〉/q)log(〈k〉/q) where 〈k〉 is the mean degree of both networks. Being this behavior is in marked contrast with a purely diffusive process, where the mixing time would go simply like 〈k〉/q, we identify the logarithmic slowing down in tx to be the result of a spontaneous mechanism of repulsion between the reactants A and B due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.
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<![CDATA[Autocorrelation of the susceptibleinfectedsusceptible process on networks]]>
https://www.researchpad.co/article/elastic_article_8191
In this paper, we focus on the autocorrelation of the susceptibleinfectedsusceptible (SIS) process on networks. The Nintertwined meanfield approximation (NIMFA) is applied to calculate the autocorrelation properties of the exact SIS process. We derive the autocorrelation of the infection state of each node and the fraction of infected nodes both in the steady and transient states as functions of the infection probabilities of nodes. Moreover, we show that the autocorrelation can be used to estimate the infection and curing rates of the SIS process. The theoretical results are compared with the simulation of the exact SIS process. Our work fully utilizes the potential of the meanfield method and shows that NIMFA can indeed capture the autocorrelation properties of the exact SIS process.
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<![CDATA[Two golden times in twostep contagion models: A nonlinear map approach]]>
https://www.researchpad.co/article/elastic_article_8188
The twostep contagion model is a simple toy model for understanding pandemic outbreaks that occur in the real world. The model takes into account that a susceptible person either gets immediately infected or weakened when getting into contact with an infectious one. As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs. The time required to reach such a pandemic outbreak allows for intervention and is often called golden time. Understanding the sizedependence of the golden time is useful for controlling pandemic outbreak. Using an approach based on a nonlinear mapping, here we find that there exist two types of golden times in the twostep contagion model, which scale as O(N1/3) and O(Nζ) with the system size N on ErdősRényi networks, where the measured ζ is slightly larger than 1/4. They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively. While the exponent 1/3 of the Ndependence of the golden time is universal even in other models showing discontinuous transitions induced by cascading dynamics, the measured ζ exponents are all close to 1/4 but show modeldependence. It remains open whether or not ζ reduces to 1/4 in the asymptotically largeN limit. Our method can be applied to several models showing a hybrid percolation transition and gives insight into the origin of the two golden times.
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<![CDATA[Correlations between thresholds and degrees: An analytic approach to model attacks and failure cascades]]>
https://www.researchpad.co/article/elastic_article_8187
Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet they are disregarded in standard analytic methods as local tree or heterogeneous mean field approximations, since order statistics are difficult to capture analytically because of their combinatorial nature. We show how they become tractable in the thermodynamic limit of infinite network size. This enables the analytic description of node attacks that are characterized by threshold allocations based on node degree. Using two examples, we discuss possible implications of irregular phase transitions and different speeds of cascade evolution for the control of cascades.
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