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The ranking of nodes in a network according to their centrality or ''importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show—as proof of concept grounded on rigorous mathematical evidence—that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn—while not eliminating the virus—this fast switching policy is sustainable over time, and it mitigates the infection until a vaccine or treatment becomes available, while alleviating the social costs associated with long lockdowns. Typically, the policy might be in the form of 1-day of work followed by 6-days of lockdown every week (or perhaps 2 days working, 5 days off) and it can be modified at a slow-rate based on measurements filtered over longer time scales. Our results highlight the potential efficacy of high frequency switching interventions in post lockdown mitigation. All code is available on Github at https://github.com/V4p1d/FPSP%5fCovid19. A software tool has also been developed so that interested parties can explore the proof-of-concept system. Author summary: Why? The design of post-lockdown mitigation policies while vaccines are still not available is pressing now as new secondary waves of the virus have emerged in many countries (for example, in Spain, France, UK, Italy, Israel, and others), and as several of these countries grapple with the reintroduction of full lockdown measures. What do we do and find? We propose efficacious and realisable methods based on control theory to tame the complex behaviour of COVID-19 in well mixed populations. We achieve this through a policy of fast intermittent lockdown intervals with regular period. We illustrate how our approach offers a fundamentally new perspective on ways to design COVID-19 exit strategies from policies of total lockdown. Our theoretical results are also very general and apply to a wide range of epidemiological models. What do these findings mean? Unlike many other proposed abatement strategies, which have risks and uncertainties possibly leading to multiple waves of infection, we demonstrate that our proposed policies have the potential to suppress the virus outbreak, while at the same time allowing continued economic activity. These policies, while of practical significance, are built on rigorous theoretical results, which are to the best of our knowledge, new in mathematical epidemiology. An extensive validation is carried out using a detailed epidemic model validated on real COVID-19 data from Italy and published very recently in Nature Medicine. [ABSTRACT FROM AUTHOR]

Testing, tracking and tracing abilities have been identified as pivotal in helping countries to safely reopen activities after the first wave of the COVID-19 virus. Contact tracing apps give the unprecedented possibility to reconstruct graphs of daily contacts, so the question is: who should be tested? As human contact networks are known to exhibit community structure, in this paper we show that the Kemeny constant of a graph can be used to identify and analyze bridges between communities in a graph. Our 'Kemeny indicator' is the value of the Kemeny constant in the new graph that is obtained when a node is removed from the original graph. We show that testing individuals who are associated with large values of the Kemeny indicator can help in efficiently intercepting new virus outbreaks, when they are still in their early stage. Extensive simulations provide promising results in early identification and in blocking the possible 'super-spreaders' links that transmit disease between different communities. [ABSTRACT FROM AUTHOR]

Summary: In this paper we propose a new design paradigm, which employs a postprocessing internal model unit, to approach the problem of output regulation for a class of multivariable minimum‐phase nonlinear systems possessing a partial normal form. Contrary to previous approaches, the proposed regulator handles control inputs of dimension larger than the number of regulated variables, provided that a controllability assumption holds, and can employ additional measurements that need not to vanish at the ideal error‐zeroing steady state, but that can be useful for stabilization purposes or to fulfill the minimum‐phase requirement. Conditions for practical and asymptotic output regulation are given, underlying how in postprocessing schemes the design of internal models is necessarily intertwined with that of the stabilizer. [ABSTRACT FROM AUTHOR]