2,098 research outputs found

    Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

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    Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work, we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time by multiple sources. In particular, we consider a (microscopic) branching network (probabilistic cellular automaton) with annealed connectivity disorder, record the macroscopic activity, and then approximate this activity by a (macroscopic) branching process. In this framework, we analytically calculate the effect of coalescence on the collective dynamics. We show that coalescence leads to a universal non-linear scaling function for the conditional expectation value of successive network activity. This allows us to quantify the difference between the microscopic model parameter and established macroscopic estimates. To overcome this difference, we propose a non-linear estimator that correctly infers the model branching parameter for all system sizes.Comment: 13 page

    Dynamic range of hypercubic stochastic excitable media

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    We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modelled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h. The response function (mean density of active sites rho versus h) is obtained via simulations (for d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels (for all d). In any dimension, the dynamic range of the response function is maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d.Comment: 7 pages, 4 figure

    Social distancing strategies against disease spreading

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    The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, i.ei.e, the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, i.ei.e, the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.Comment: to be published in "Perspectives and Challenges in Statistical Physics and Complex Systems for the Next Decade", Word Scientific Pres

    Inferring collective dynamical states from widely unobserved systems

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    When assessing spatially-extended complex systems, one can rarely sample the states of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating events. We derive a subsampling-invariant estimator, and demonstrate that it correctly infers the infectiousness of various diseases under subsampling, making it particularly useful in countries with unreliable case reports. In neuroscience, recordings are strongly limited by subsampling. Here, the subsampling-invariant estimator allows to revisit two prominent hypotheses about the brain's collective spiking dynamics: asynchronous-irregular or critical. We identify consistently for rat, cat and monkey a state that combines features of both and allows input to reverberate in the network for hundreds of milliseconds. Overall, owing to its ready applicability, the novel estimator paves the way to novel insight for the study of spatially-extended dynamical systems.Comment: 7 pages + 12 pages supplementary information + 7 supplementary figures. Title changed to match journal referenc

    Critical fluctuations in epidemic models explain COVID‑19 post‑lockdown dynamics

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    As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate β is not signifcantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, β>βc) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, β<βc) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with r(t) ≈ 1 hovering around its threshold value.BMTF “Mathematical Modeling Applied to Health” Project European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 79249
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