In this work, we propose to define a new space that will be called locally Cartesian space (Saidou'Spaces). It is a space defined by a new topology whose fundamental system of neighborhood are compact cartesian subsets, theses subsets were already defined during our previous work, "Geometrical introduction to Cartesian geometry in complex shapes see [15]. It will have the same properties of a Banach space. Then, we will give the steps of a cartesianization method of complex shapes or region in this space. The objective sought by this technique is to find a cartesian form (denoted Car(A)), that approximates any form A, see Figure1 below. It should be noted that cartesianization will be a generalization of the polygonization whish remains the object of research for several researchers in the spaces R 2 Ref [12] [13] [6].
The Cartesian word or "Cartesianity" was born with the philosophy of Descart (1596-1650). He was at the base of a doctrine based on rationalism, that it is means the search for truth by reason. Among others, Sigmend Freud had also approached this notion of psychological point to study the enigma of thoughts in humans. Other aspects of the Cartesian word have been used in mathematical geometry, namely cartesian coordinates and Cartesian referentials. As you know, studying a shape with curved and enclosed borders is more complicated than working on shapes with linear borders without curvature. In the way, we will introduce to the Cartesian geometry and characterize he Cartesian shapes.
Background
COVID-19 caused a worldwide outbreak leading the majority of human activities to a rough breakdown. Many stakeholders proposed multiple interventions to slow down the disease and number of papers were devoted to the understanding the pandemic, but to a less extend some were oriented socio-economic analysis. In this paper, a socio-economic analysis is proposed to investigate the early-age effect of socio-economic factors on COVID-19 spread.
Methods
Fifty-two countries were selected for this study. A cascade algorithm was developed to extract the R0 number and the day J*; these latter should decrease as the pandemic flattens. Subsequently, R0 and J* were modeled according to socio-economic factors using multilinear stepwise-regression.
Results
The findings demonstrated that low values of days before lockdown should flatten the pandemic by reducing J*. Hopefully, DBLD is only parameter to be tuned in the short-term; the other socio-economic parameters cannot easily be handled as they are annually updated. Furthermore, it was highlighted that the elderly is also a major influencing factor especially because it is involved in the interactions terms in R0 model. Simulations proved that the health care system could improve the pandemic damping for low elderly. In contrast, above a given elderly, the reproduction number R0 cannot be reduced even for developed countries (showing high HCI values), meaning that the disease’s severity cannot be smoothed regardless the performance of the corresponding health care system; non-pharmaceutical interventions are then expected to be more efficient than corrective measures.
Discussion
The relationship between the socio-economic factors and the pandemic parameters R0 and J* exhibits complex relations compared to the models that are proposed in the literature. The quadratic regression model proposed here has discriminated the most influencing parameters within the following approximated order, DLBL, HCI, Elderly, Tav, CO2, and WC as first order, interaction, and second order terms.
Conclusions
This modeling allowed the emergence of interaction terms that don’t appear in similar studies; this led to emphasize more complex relationship between the infection spread and the socio-economic factors. Future works will focus on enriching the datasets and the optimization of the controlled parameters to short-term slowdown of similar pandemics.
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