Modeling the Spatiotemporal Epidemic Spreading of COVID-19 and the Impact of Mobility and Social Distancing Interventions

On 31 December, 2019, an outbreak of a novel coronavirus, SARS-CoV-2, that causes the COVID-19 disease, was first reported in Hubei, mainland China. This epidemics'' health threat is probably one of the biggest challenges faced by our interconnected modern societies. According to the epidemiological reports, the large basic reproduction number R0~3.0, together with a huge fraction of asymptomatic infections, paved the way for a major crisis of the national health capacity systems. Here, we develop an age-stratified mobility-based metapopulation model that encapsulates the main particularities of the spreading of COVID-19 regarding (i) its transmission among individuals, (ii) the specificities of certain demographic groups with respect to the impact of COVID-19, and (iii) the human mobility patterns inside and among regions. The full dynamics of the epidemic is formalized in terms of a microscopic Markov chain approach that incorporates the former elements and the possibility of implementing containment measures based on social distancing and confinement. With this model, we study the evolution of the effective reproduction number R(t), the key epidemiological parameter to track the evolution of the transmissibility and the effects of containment measures, as it quantifies the number of secondary infections generated by an infected individual. The suppression of the epidemic is directly related to this value and is attained when R<1. We find an analytical expression connecting R with nonpharmacological interventions, and its phase diagram is presented. We apply this model at the municipality level in Spain, successfully forecasting the observed incidence and the number of fatalities in the country at each of its regions. The expression for R should assist policymakers to evaluate the epidemics'' response to actions, such as enforcing or relaxing confinement and social distancing

The physics of spreading processes in multilayer networks

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.Comment: 25 pages, 4 figure

Competing spreading processes on multiplex networks: Awareness and epidemics

10.1103/PhysRevE.90.012808Epidemiclike spreading processes on top of multilayered interconnected complex networks reveal a rich phase diagram of intertwined competition effects. A recent study by the authors [C. Granell, Phys. Rev. Lett. 111, 128701 (2013).PRLTAO0031-900710.1103/PhysRevLett.111.128701] presented an analysis of the interrelation between two processes accounting for the spreading of an epidemic, and the spreading of information awareness to prevent infection, on top of multiplex networks. The results in the case in which awareness implies total immunization to the disease revealed the existence of a metacritical point at which the critical onset of the epidemics starts, depending on completion of the awareness process. Here we present a full analysis of these critical properties in the more general scenario where the awareness spreading does not imply total immunization, and where infection does not imply immediate awareness of it. We find the critical relation between the two competing processes for a wide spectrum of parameters representing the interaction between them. We also analyze the consequences of a massive broadcast of awareness (mass media) on the final outcome of the epidemic incidence. Importantly enough, the mass media make the metacritical point disappear. The results reveal that the main finding, i.e., existence of a metacritical point, is rooted in the competition principle and holds for a large set of scenarios

Unsupervised clustering analysis: a multiscale complex networks approach

10.1142/S021812741230023

Muscle tenderness and psychiatric comorbidity: a vicious cycle in migraine chronicization.

10.3390/e15125464Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural properties. The finding of structural patterns is of utmost importance to reduce the problem of understanding the structure¿function relationships. Here we propose the analysis of similarity measures between nodes using hierarchical clustering methods. The discrete nature of the networks usually leads to a small set of different similarity values, making standard hierarchical clustering algorithms ambiguous. We propose the use of multidendrograms, an algorithm that computes agglomerative hierarchical clusterings implementing a variable-group technique that solves the non-uniqueness problem found in the standard pair-group algorithm. This problem arises when there are more than two clusters separated by the same maximum similarity (or minimum distance) during the agglomerative process. Forcing binary trees in this case means breaking ties in some way, thus giving rise to different output clusterings depending on the criterion used. Multidendrograms solves this problem by grouping more than two clusters at the same time when ties occur

A spectral algorithm of community identification

10.1209/0295-5075/101/48001EPL1014