Highlights

 

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 it 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.

 

 

Alberto Aleta, and Yamir Moreno, “Evaluation of the potential incidence of COVID-19 and effectiveness of contention measures in Spain: a data-driven approach”, BMC Medicine 18:157 (2020).

 

This book provides the basis of a formal language and explores its possibilities in the characterization of multiplex networks. Armed with the formalism developed, the authors define structural metrics for multiplex networks. A methodology to generalize monoplex structural metrics to multiplex networks is also presented so that the reader will be able to generalize other metrics of interest in a systematic way. Therefore, this book will serve as a guide for the theoretical development of new multiplex metrics. Furthermore, this Brief describes the spectral properties of these networks in relation to concepts from algebraic graph theory and the theory of matrix polynomials. The text is rounded off by analyzing the different structural transitions present in multiplex systems as well as by a brief overview of some representative dynamical processes. Multiplex Networks will appeal to students, researchers, and professionals within the fields of network science, graph theory, and data science.

 

 

E. Cozzo, G. Ferraz de Arruda, F. A. Rodrigues, and Y. Moreno, “Multiplex Networks: Basic Formalism and Structural Properties”, Monograph Springer Briefs in Complexity, ISBN 978-3-319-92255-3 (2018).

[PNAS 115, E3238-E3245 (2018).]

 

In the case of tuberculosis (TB), the capabilities of epidemic models to produce quantitatively robust forecasts are limited by multiple hindrances. Among these, understanding the complex relationship between disease epidemiology and populations’ age structure has been highlighted as one of the most relevant. TB dynamics depends on age in multiple ways, some of which are traditionally simplified in the literature. That is the case of the heterogeneities in contact intensity among different age strata that are common to all airborne diseases, but still typically neglected in the TB case. Furthermore, while demographic structures of many countries are rapidly aging, demographic dynamics are pervasively ignored when modeling TB spreading. In this work, we present a TB transmission model that incorporates country-specific demographic prospects and empirical contact data around a data-driven description of TB dynamics. Using our model, we find that the inclusion of demographic dynamics is followed by an increase in the burden levels predicted for the next decades in the areas of the world that are most hit by the disease today. Similarly, we show that considering realistic patterns of contacts among individuals in different age strata reshapes the transmission patterns reproduced by the models, a result with potential implications for the design of age-focused epidemiological interventions.

 

Sergio Arregui, Dessislava Marinova, Maria Jose Iglesias, Sofia Samper, Carlos Martin, Joaquin Sanz, and Yamir Moreno, “Data-driven model for the assessment of M. Tuberculosis transmission in evolving demographic structures”, Proceedings of the National Academy of Sciences USA 115, E3238-E3245 (2018).

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[PRX 7:011014, 2017]

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible- infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes.

 

G. Ferraz de Arruda, E. Cozzo, T. P. Peixoto, F. A. Rodrigues, and Y. Moreno, “Disease Localization in Multilayer Networks”, Physical Review X 7, 011014 (2017).

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[PRX 4:041005, 2014; Plos Comp. Biol. 9:e1003169, 2013] The advances in the realism of epidemic modeling are however hampered by our current limitations to properly deal with several factors such as: real demographic distributions, detailed migration and mobility patterns, human behavioral responses to the presence of an outbreak, disease’s multi-strain, and the concurrency of several diseases, among others.

Most epidemic models assume that the spreading process takes place on a single level (be it a single population, a meta-population system or a network of contacts). The latter results from our current limited knowledge about the interplay among the various scales involved in the transmission of infectious diseases at the global scale. Therefore, pressing problems rooted at the interdependency of multi-scales call for the development of a whole new set of theoretical and simulation approaches. It is extremely importatnt to develop disease-specific theoretical and computational models to understand the transmission mechanisms behind global public health threats. The fact of considering the interdependency between many levels and scales represents a radical change that makes a substantial difference as it allows addressing problems such as comorbidity and the spreading of persistent infections and multi-strain diseases. Thus, the goal consists of developing a contemporary epidemiological framework that integrates the many aspects involved in the spreading of global diseases: from single networks of contacts to meta-population systems and from the interaction between different diseases and strains to the influence of human behavioral changes and mobility patterns.

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In this paper, we develop a theoretical and computational framework to study the dynamics of concurrent diseases. We propose a model for the description of the simultaneous spreading of two interacting pathogens on the same host population through independent contact networks. The model is based on an heterogenous mean-field approach to describe the critical properties of the dynamics as well as an adequate framework for the temporal description of coupled out of equilibrium outbreaks for both the Susceptible-Infected-Susceptible and Susceptible-Infected-Removed scenarios. The proposed framework allows to analytically derive the epidemic thresholds of the diseases modeled, explicitly addressing the influence on each threshold on aspects such as the prevalence of the conjugate disease, the system size, the architecture of the networks of contacts and the appearance of eventual correlations between them.

Overall, our findings provide deep insights into what are the key mechanisms that drive the evolution of interacting diseases and secondly, they pave the way for the development of quantitative, data-driven models for the detailed characterization of concurrent and interacting diseases.

 

J. Sanz, C.-Y. Xia, S. Meloni and Y. Moreno, “Dynamics of interacting diseases”, Physical Review X 4, 041005 (2014).

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However, the available data on human mobility and interaction are descriptive of human behavior as long as information concerning the unfolding of the epidemic does not induce changes in the population’s behavior, for at this point the model has to include the population’s behavioral changes that in turn alter the epidemic spreading.

In particular, self-initiated behavioral changes are elusive to modeling because of the difficulty involved in quantifying these changes and an overall lack of relevant data. Although there have been some attempts to develop formal models, only a few of these theoretical and computational approaches have considered the spatially structured nature of populations. Therefore, the effect of behavioral and mobility changes in the large-scale spreading of the epidemic is still an open problem. It is thus of utmost importance to further investigate into this issue.

 

S. Meloni, N. Perra, A. Arenas, S. Gomez, Y. Moreno, and A. Vespignani, “Modeling Human Mobility Responses to the Large-scale Spreading of Infectious Diseases”, Scientific Reports 1, 62 (2011).

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These models are most needed to study complex disease contagion. In an increasingly globalized world, in which population movements are becoming more frequent and massive, we must realize that what happens anywhere in the world has an impact on our environment. It is therefore the time to develop models that address the effects of the interaction between multiple strains in structured populations. Their integration into current theoretical and modeling efforts to aid our understanding of the mechanisms of transmission and evaluation of potential control strategies constitutes one of the main goals.

To study the dynamics of multi-strain epidemics, one has to extend the traditional framework to consider multiple strains of a disease spreading through one host species. This kind of models is in its early infancy, as the scientific community is only starting to understand the wide spectrum of complex outcomes that result from the competition of multiple strains for a limited number of susceptible individuals in unstructured populations. The need to address the issue of multiple strains’ interactions is becoming increasingly recognized as one of the most fundamental open problems in modern epidemiology and public health.

 

C. Poletto, S. Meloni, V. Colizza, Y. Moreno and A. Vespignani, “Host mobility drives pathogen competition in spatially structured populations”, PLoS Computational Biology 9 (8): e1003169 (2013).

C. Poletto, S. Meloni, A. Van Metre, V. Colizza, Y. Moreno and A. Vespignani, “Characterizing two-pathogen competition in spatially structured environments”, Scientific Reports 5:7895 (2015).

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However, in specific realizations of a model’s topology (quenched networks), HMF can result in different levels of accuracy. This problem leads to the question of whether or not the direct use of the HMF approach is accurate enough when dealing with real networks. On the other hand, meta-population approaches are an essential theoretical framework used in Epidemiology, population ecology, genetics and adaptive evolution to describe population dynamics whenever the spatial structure of populations plays an important role in the system’s evolution.

The basic assumption of meta-population models is that the system under study is highly fragmented and characterized by populations localized in relatively isolated discrete units/subpopulations connected by some degree of migration and or commuting. Two different dynamics take place concurrently: inside each subpopulation and between subpopulations. The most important difference with respect to single population models is the existence of a second epidemic threshold. This new critical point, known as global invasion threshold, marks the point beyond which a local outbreak reaches other subpopulations and spreads throughout the meta-population system. The global invasion point does not only depend on the infection parameters, but also on the mobility rates of individuals as well and thus differs from the single population epidemic threshold.

Recent works have extensively applied meta-population schemes to understand the epidemic dynamics of spatially structured populations. However, theoretical approaches are all at the mean-field level and use a tree-like approximation that represents the evolution of the number of diseased subpopulations as a branching process. In addition, individuals within the subpopulations are all well mixed and no sources of heterogeneity (neither in the networks of contacts nor in the individual mobility rates) at the lower individual scale are built in the models. Finally, data-driven computations are very intensive and lengthy, especially when modeling disease propagation worldwide. We therefore aim at integrating individual-level approaches into meta-population schemes to add further realism to the structure of subpopulations.