While severe social-distancing measures have proven effective in slowing the coronavirus disease 2019 (COVID-19) pandemic, second-wave scenarios are likely to emerge as restrictions are lifted. Here we integrate anonymized, geolocalized mobility data with census and demographic data to build a detailed agent-based model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission in the Boston metropolitan area. We find that a period of strict social distancing followed by a robust level of testing, contact-tracing and household quarantine could keep the disease within the capacity of the healthcare system while enabling the reopening of economic activities. Our results show that a response system based on enhanced testing and contact tracing can have a major role in relaxing social-distancing interventions in the absence of herd immunity against SARS-CoV-2.

SignificanceThe analysis of real epidemiological data has raised issues of the adequacy of the classic homogeneous modeling framework and quantities, such as the basic reproduction number in real-world situations. Based on high-quality sociodemographic data, here we generate a multiplex network describing the contact pattern of the Italian and Dutch populations. By using a microsimulation approach, we show that, for epidemics spreading on realistic contact networks, it is not possible to define a steady exponential growth phase and a basic reproduction number. We show the operational use of the instantaneous reproduction rate as a good descriptor of the transmission dynamics.

The new coronavirus disease 2019 has required the implementation of severe mobility restrictions and social distancing measures worldwide. While these measures have been proven effective in abating the epidemic in several countries, it is important to estimate the effectiveness of testing and tracing strategies to avoid a potential second wave of the COVID-19 epidemic. We integrate highly detailed (anonymized, privacy-enhanced) mobility data from mobile devices, with census and demographic data to build a detailed agent-based model to describe the transmission dynamics of SARS-CoV-2 in the Boston metropolitan area. We find that enforcing strict social distancing followed by a policy based on a robust level of testing, contact-tracing and household quarantine, could keep the disease at a level that does not exceed the capacity of the health care system. Assuming the identification of 50% of the symptomatic infections, and the tracing of 40% of their contacts and households, which corresponds to about 9% of individuals quarantined, the ensuing reduction in transmission allows the reopening of economic activities while attaining a manageable impact on the health care system. Our results show that a response system based on enhanced testing and contact tracing can play a major role in relaxing social distancing interventions in the absence of herd immunity against SARS-CoV-2.The first report of a new infectious disease, later coined COVID-19, appeared on 31 December 2019 1 . As of 2 May 2020, the virus has spread to 187 countries with more than 3.4 millions confirmed cases worldwide, and killing more than 240,000 people 2 . As the number of confirmed 2 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's constituents. During the last two decades, network science has provided many insights in natural, social, biological and technological systems. However, real systems are more often than not interconnected, with many interdependencies that are not properly captured by single layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.

The modeling of large-scale communicable epidemics has greatly benefited in the last years from the increasing availability of highly detailed data. Particullarly, in order to achieve quantitative descriptions of the evolution of epidemics, contact networks and mixing patterns are key. These heterogeneous patterns depend on several factors such as location, socioeconomic conditions, time, and age. This last factor has been shown to encapsulate a large fraction of the observed inter-individual variation in contact patterns, an observation validated by different measurements of age-dependent contact matrices. Recently, several works have studied how to project those matrices to areas where empirical data are not available. However, the dependence of contact matrices on demographic structures and their time evolution has been largely neglected. In this work, we tackle the problem of how to transform an empirical contact matrix that has been obtained for a given demographic structure into a different contact matrix that is compatible with a different demography. The methodology discussed here allows to extrapolate a contact structure measured in a particular area to any other whose demographic structure is known, as well as to obtain the time evolution of contact matrices as a function of the demographic dynamics of the populations they refer to. To quantify the effect of considering time-dynamics of contact patterns on disease modeling, we implemented a Susceptible-Exposed-Infected-Recovered (SEIR) model on 16 different countries and regions and evaluated the impact of neglecting the temporal evolution of mixing patterns. Our results show that simulated disease incidence rates, both at the aggregated and age-specific levels, are significantly dependent on contact structures variation driven by demographic evolution. The present work opens the path to eliminate technical biases from model-based impact evaluations of future epidemic threats and warns against the use of contact matrices to model diseases without correcting for demographic evolution or geographic variations.

Public urban mobility systems are composed by several transportation modes connected together. Most studies in urban mobility and planning often ignore the multi-layer nature of transportation systems considering only aggregated versions of this complex scenario. In this work we present a model for the representation of the transportation system of an entire city as a multiplex network. Using two different perspectives, one in which each line is a layer and one in which lines of the same transportation mode are grouped together, we study the interconnected structure of 9 different cities in Europe raging from small towns to mega-cities like London and Berlin highlighting their vulnerabilities and possible improvements. Finally, for the city of Zaragoza in Spain, we also consider data about service schedule and waiting times, which allow us to create a simple yet realistic model for urban mobility able to reproduce real-world facts and to test for network improvements.

Background We are currently experiencing an unprecedented challenge, managing and containing an outbreak of a new coronavirus disease known as COVID-19. While China—where the outbreak started—seems to have been able to contain the growth of the epidemic, different outbreaks are nowadays present in multiple countries. Nonetheless, authorities have taken action and implemented containment measures, even if not everything is known. Methods To facilitate this task, we have studied the effect of different containment strategies that can be put into effect. Our work referred initially to the situation in Spain as of February 28, 2020, where a few dozens of cases had been detected, but has been updated to match the current situation as of 13 April. We implemented an SEIR metapopulation model that allows tracing explicitly the spatial spread of the disease through data-driven stochastic simulations. Results Our results are in line with the most recent recommendations from the World Health Organization, namely, that the best strategy is the early detection and isolation of individuals with symptoms, followed by interventions and public recommendations aimed at reducing the transmissibility of the disease, which, although might not be sufficient for disease eradication, would produce as a second order effect a delay of several days in the raise of the number of infected cases. Conclusions Many quantitative aspects of the natural history of the disease are still unknown, such as the amount of possible asymptomatic spreading or the role of age in both the susceptibility and mortality of the disease. However, preparedness plans and mitigation interventions should be ready for quick and efficacious deployment globally. The scenarios evaluated here through data-driven simulations indicate that measures aimed at reducing individuals’ flow are much less effective than others intended for early case identification and isolation. Therefore, resources should be directed towards detecting as many and as fast as possible the new cases and isolate them.

The modeling of large-scale communicable epidemics has greatly benefited in the last years from the increasing availability of highly detailed data. Particularly, in order to achieve quantitative descriptions of the evolution of epidemics, contact networks and mixing patterns are key. These heterogeneous patterns depend on several factors such as location, socioeconomic conditions, time, and age. This last factor has been shown to encapsulate a large fraction of the observed inter-individual variation in contact patterns, an observation validated by different measurements of age-dependent contact matrices. Recently, several works have studied how to project those matrices to areas where empiric data is not available. However, the dependence of contact matrices on demographic structures and their time evolution has been largely neglected. In this work, we tackle the problem of how to transform an empirical contact matrix that has been obtained for a given demographic structure into a different contact matrix that is compatible with a different demography. The methodology discussed here allows extrapolating a contact structure measured in a particular area to any other whose demographic structure is known, as well as to obtain the time evolution of contact matrices as a function of the demographic dynamics of the populations they refer to. To quantify the effect of considering time-dynamics of contact patterns on disease modeling, we implemented a Susceptible-Exposed-Infected-Recovered (SEIR) model on 16 different countries and evaluated the impact of neglecting the temporal evolution of mixing patterns. Our results show that simulated disease incidence rates, both at the aggregated and age-specific levels, are significantly dependent on contact structures variation driven by demographic evolution. The present work opens the path to eliminate technical biases from model-based impact evaluations of future epidemic threats and warns against the use of contact matrices to model diseases without correcting for demographic evolution or geographic variations. Author summaryLarge scale epidemic outbreaks represent an ever increasing threat to humankind. In order to anticipate eventual pandemics, mathematical modeling should not only have the capacity to model in real time an ongoing disease, but also to predict the evolution June 11, 2018 1/16 of potential outbreaks in different locations and times. To this end, computational frameworks need to incorporate, among other ingredients, realistic contact patterns into the models. This not only implies anticipating the demographic structure of the populations under study, but also understanding how demographic evolution reshapes social mixing patterns along time. Here we present a mathematical framework to solve this problem and test our modeling approach on 16 different empirical contact matrices. We also evaluate the impact of an eventual future outbreak by simulating a SEIR scenario in the countries analyzed. Our results show that using outdated or imported contact matrices ...