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In this research work, we propose to assess the dynamic correlation between different mobility indices, measured on a daily basis, and the new cases of COVID-19 in the different Portuguese districts. The analysis is based on global correlation measures, which capture linear and non-linear relationships in time series, in a robust and dynamic way, in a period without significant changes of non-pharmacological measures. The results show that mobility in retail and recreation, grocery and pharmacy, and public transport shows a higher correlation with new COVID-19 cases than mobility in parks, workplaces or residences. It should also be noted that this relationship is lower in districts with lower population density, which leads to the need for differentiated confinement policies in order to minimize the impacts of a terrible economic and social crisis.

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This work investigates the possibility of suppressing chaos in a fractional-nonlinear macroeconomic dynamic model. The system generalizes a model recently reported in the literature in which chaos is strongly present. This description involves the inclusion of the public sector deficit and its coupling with other variables. The system is simulated for integer and non-integer orders that produce a complex dynamics. The time histories and the phase diagrams are presented. The main contribution of this work refers to the adoption of the largest Lyapunov exponent (LLE) criteria based on Wolf's algorithm. This approach improves the response of the system, suppressing, at least partially, the strong presence of chaos reported in previous studies. c