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In this manuscript, we point out that the federal government headed by President Bolsonaro has pursued a political agenda that contributed to the spread of COVID-19, transforming the country into a major repository for SARS-CoV-2 and its variants, thus representing a risk for worldwide containment efforts. Furthermore his actions are also weakening democratic institutions, which could counter his political agenda, effectively facilitating the spread of COVID-19. Thus, the perpetuation of the COVID-19 pandemic in Brazil is due to human behaviour factors, especially high-level public decision makers.

Considering numerical simulations, this study shows that the so-called vertical social distancing health policy is ineffective to contain the COVID-19 pandemic. We present the SEIR-Net model, for a network of social group interactions, as a development of the classic mathematical model of SEIR epidemics (Susceptible-Exposed-Infected (symptomatic and asymptomatic)-Removed). In the SEIR-Net model, we can simulate social contacts between groups divided by age groups and analyze different strategies of social distancing. In the vertical distancing policy, only older people are distanced, whereas in the horizontal distancing policy all age groups adhere to social distancing. These two scenarios are compared to a control scenario in which no intervention is made to distance people. The vertical distancing scenario is almost as bad as the control, both in terms of people infected and in the acceleration of cases. On the other hand, horizontal distancing, if applied with the same intensity in all age groups, significantly reduces the total infected people “flattening the disease growth curve”. Our analysis considers the city of Belo Horizonte, Minas Gerais State, Brazil, but similar conclusions apply to other cities as well. Code implementation of the model in R-language is provided in the supplementary material.

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We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L 2 (R 2 ) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [0,1], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness reaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.