RESUMEN

The recent Covid-19 epidemic has pointed out the inadequacy of the plans applied by industrial countries to limit the epidemic spread and frailty of the global economy to cope with a pandemic. Many countries were forced to a global lockdown with a great socio-economic impact. In Italy, one of the problems was the complex mobility network structure of the Northern regions that made ineffective the attempts to isolate the initial hotspots. In the paper we study a simple model that simulates the epidemic spread on a community network that may exchange population according to a daily mobility rate. In each community the epidemic evolution is provided by a stochastic compartmental model whose parameters are tuned to reproduce the Covid-19 evolution observed in Italy before the global lockdown policies. We initially study the delay in the epidemic spread due to the finite local mobility by proposing a power law relation for the increasing of the infection peak time in each node and the network distance from the initial node where the epidemic starts. We consider two scenarios to study the effectiveness of local lockdown policies: the presence of two clusters weakly connected by the mobility or a homogeneous chain of communities that exchange the population at a fixed rate. In both cases we show the existence of a threshold effect, in a probabilistic sense, for the effectiveness of lockdown policies as a function of the delay time at which such policies are applied, or of the network distance from the outbreak node.

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RESUMEN

Recent studies of human mobility largely focus on displacements patterns and power law fits of empirical long-tailed distributions of distances are usually associated to scale-free superdiffusive random walks called Lévy flights. However, drawing conclusions about a complex system from a fit, without any further knowledge of the underlying dynamics, might lead to erroneous interpretations. Here we show, on the basis of a data set describing the trajectories of 780,000 private vehicles in Italy, that the Lévy flight model cannot explain the behaviour of travel times and speeds. We therefore introduce a class of accelerated random walks, validated by empirical observations, where the velocity changes due to acceleration kicks at random times. Combining this mechanism with an exponentially decaying distribution of travel times leads to a short-tailed distribution of distances which could indeed be mistaken with a truncated power law. These results illustrate the limits of purely descriptive models and provide a mechanistic view of mobility.

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RESUMEN

Valuable information for estimating the traffic flow is obtained with current GPS technology by monitoring position and velocity of vehicles. In this paper, we present a proof of concept study that shows how the traffic state can be estimated using only partial and noisy data by assimilating them in a dynamical model. Our approach is based on a data assimilation algorithm, developed by the authors for chaotic geophysical models, designed to be equivalent but computationally much less demanding than the traditional extended Kalman filter. Here we show that the algorithm is even more efficient if the system is not chaotic and demonstrate by numerical experiments that an accurate reconstruction of the complete traffic state can be obtained at a very low computational cost by monitoring only a small percentage of vehicles.