Epidemic processes are common out-of-equilibrium phenomena of broad interdisciplinary interest. Recently, dynamic message-passing (DMP) has been proposed as an efficient algorithm for simulating epidemic models on networks, and in particular for estimating the probability that a given node will become infectious at a particular time. To date, DMP has been applied exclusively to models with one-way state changes, as opposed to models like SIS and SIRS where nodes can return to previously inhabited states. Because many real-world epidemics can exhibit such recurrent dynamics, we propose a DMP algorithm for complex, recurrent epidemic models on networks. Our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids echo chamber effects'' where a pair of adjacent nodes each amplify the probability that the other is infectious. We demonstrate that this approach well approximates results obtained from Monte Carlo simulation and that its accuracy is often superior to the pair approximation (which also takes second-order correlations into account). Moreover, our approach is more computationally efficient than the pair approximation, especially for complex epidemic models: the number of variables in our DMP approach grows as @math where @math is the number of edges and @math is the number of states, as opposed to @math for the pair approximation. We suspect that the resulting reduction in computational effort, as well as the conceptual simplicity of DMP, will make it a useful tool in epidemic modeling, especially for high-dimensional inference tasks.
Similarly, just as the leading eigenvector of @math was recently shown to be a good measure of importance or centrality'' of a node @cite_50 , it may be helpful in identifying superspreaders''---nodes where an initial infection will generate the largest outbreak, and be the most likely to lead to a widespread epidemic.
@cite_50
2161283706 1992250165 2963123334 1964241922
Simulation studies using susceptible-infectious-recovered models were conducted to estimate individuals’ risk of infection and time to infection in small-world and randomly mixing networks. Infection transmitted more rapidly but ultimately resulted in fewer infected individuals in the small-world, compared with the random, network. The ability of measures of network centrality to identify high-risk individuals was also assessed. ‘‘Centrality’’ describes an individual’s position in a population; numerous parameters are available to assess this attribute. Here, the authors use the centrality measures degree (number of contacts), random-walk betweenness (a measure of the proportion of times an individual lies on the path between other individuals), shortest-path betweenness (the proportion of times an individual lies on the shortest path between other individuals), and farness (the sum of the number of steps between an individual and all other individuals). Each was associated with time to infection and risk of infection in the simulated outbreaks. In the networks examined, degree (which is the most readily measured) was at least as good as other network parameters in predicting risk of infection. Identification of more central individuals in populations may be used to inform surveillance and infection control strategies. Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible–Infected–Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes. Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with @math nodes as a sequence of @math layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supracentrality matrix of size @math whose dominant eigenvector gives the centrality of each node @math at each time @math . We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node @math and the time layer @math . We also introduce the concepts of marginal and conditional... Estimating which nodes are the infection sources that introduce a virus or rumor into a network, or the locations of pollutant sources, plays a critical role in limiting the potential damage to the network through timely quarantine of the sources. In this paper, we derive estimators for the infection sources and their infection regions based on the infection network geometry. We show that in a geometric tree with at most two sources, our estimator identifies these sources with probability going to one as the number of infected nodes increases. We extend and generalize our methods to general graphs, where the number of infection sources are unknown and there may be multiple sources. Numerical results are presented to verify the performance of our proposed algorithms under different types of graph structures.