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Register a new userEfficient reconstruction of transmission probabilities in a spreading process from partial observations
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An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the estimation of spreading parameters, based on the maximization of the likelihood of observed cascades, assuming that the full information for all the nodes in the network is available. In this work, we focus on a more realistic and restricted scenario, in which only a partial information on the cascades is available: either the set of activation times for a limited number of nodes, or the states of nodes for a subset of observation times. To tackle this problem, we first introduce a framework based on the maximization of the likelihood of the incomplete diffusion trace. However, we argue that the computation of this incomplete likelihood is a computationally hard problem, and show that a fast and robust reconstruction of transmission probabilities in sparse networks can be achieved with a new algorithm based on recently introduced dynamic message-passing equations for the spreading processes. The suggested approach can be easily generalized to a large class of discrete and continuous dynamic models, as well as to the cases of dynamically-changing networks and noisy information.
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Recently, the impacts of spatiotemporal heterogeneities of human activities on spreading dynamics have attracted extensive attention. In this paper, to study heterogeneous response times on information spreading, we focus on the susceptible-infected spreading dynamics with adjustable power-law response time distribution based on uncorrelated scale-free networks. We find that the stronger the heterogeneity of response times is, the faster the information spreading is in the early and middle stages. Following a given heterogeneity, the procedure of reducing the correlation between the response times and degrees of individuals can also accelerate the spreading dynamics in the early and middle stages. However, the dynamics in the late stage is slightly more complicated, and there is an optimal value of the full prevalence time changing with the heterogeneity of response times and the response time-degree correlation, respectively. The optimal phenomena results from the efficient allocation of heterogeneous response times.
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found that as in static networks, rewiring networks with degree distribution exponent $gamma >3$ exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For $2<gamma leq 3$ no such threshold exists, but for small infection rate the steady state density of infected nodes (prevalence) is smaller for rewiring networks.
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic parameters that do not accurately represent person-to-person variability. To address this issue, we present a dynamic network model that provides a straightforward way to incorporate both disease transmission dynamics at the individual scale as well as the full spatiotemporal history of infection at the population scale. We find that disease spreads through a social network as a traveling wave of infection, followed by a traveling wave of recovery, with the onset and dynamics of spreading determined by the interplay between disease transmission and recovery. We use these insights to develop a scaling theory that predicts the dynamics of infection for diverse diseases and populations. Furthermore, we show how spatial heterogeneities in susceptibility to infection can either exacerbate or quell the spread of disease, depending on its infectivity. Ultimately, our dynamic network approach provides a simple way to model disease spreading that unifies previous findings and can be generalized to diverse diseases, containment strategies, seasonal conditions, and community structures.
We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.
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