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A reply to the comment by Lee et al. [arXiv:1309.5367]
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Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading dynamics, edges with different weights may play far different roles: a friend from afar usually brings novel stories, and an intimate relationship is highly risky for a flu epidemic. In this article, we propose a weighted susceptible-infected-susceptible model on complex networks, where the weight of an edge is defined by the topological proximity of the two associated nodes. Each infected individual is allowed to select limited number of neighbors to contact, and a tunable parameter is introduced to control the preference to contact through high-weight or low-weight edges. Experimental results on six real networks show that the epidemic prevalence can be largely promoted when strong ties are favored in the spreading process. By comparing with two statistical null models respectively with randomized topology and randomly redistributed weights, we show that the distribution pattern of weights, rather than the topology, mainly contributes to the experimental observations. Further analysis suggests that the weight-weight correlation strongly affects the results: high-weight edges are more significant in keeping high epidemic prevalence when the weight-weight correlation is present.
Cator and Van Mieghem [Cator E, Van Mieghem P., Phys. Rev. E 89, 052802 (2014)] stated that the correlation of infection at the same time between any pair of nodes in a network is non-negative for the Markovian SIS and SIR epidemic models. The arguments used to obtain this result rely strongly on the graphical construction of the stochastic process, as well as the FKG inequality. In this note we show that although the approach used by the authors applies to the SIS model, it cannot be used for the SIR model as stated in their work. In particular, we observe that monotonicity in the process is crucial for invoking the FKG inequality. Moreover, we provide an example of simple graph for which the nodal infection in the SIR Markovian model is negatively correlated.
Metapopulation epidemic models describe epidemic dynamics in networks of spatially distant patches connected with pathways for migration of individuals. In the present study, we deal with a susceptible-infected-recovered (SIR) metapopulation model where the epidemic process in each patch is represented by an SIR model and the mobility of individuals is assumed to be a homogeneous diffusion. Our study focuses on two types of patches including high-risk and low-risk ones, in order to evaluate intervention strategies for epidemic control. We theoretically analyze the intervention threshold, indicating the critical fraction of low-risk patches for preventing a global epidemic outbreak. We show that targeted intervention to high-degree patches is more effective for epidemic control than random intervention. The theoretical results are validated by Monte Carlo simulation for synthetic and realistic scale-free patch networks. Our approach is useful for exploring better local interventions aimed at containment of epidemics.
The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations coming from that if one node is occupied, or infected (for disease spreading models), then its neighbors are likely to be occupied. By combining two theoretical approaches---the heterogeneous mean-field theory and the effective degree method---we are able to include these correlations in an analytical solution of the SIS model. We derive accurate expressions for the average prevalence (fraction of infected) and epidemic threshold. We also discuss how to generalize the approach to a larger class of stochastic population models.
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.
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