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| - Objectives: The present COVID-19 pandemic (C19P) is challenging our socities all over the world. In this work, based on massive health information daily updated, the C19P daily death numbers at a global level, are modelled, analyzed and forecasted. Methods: Two empirical models are proposed to explain daily death (DD) records: a) self-similar (SS) recurrences of the global responses, and b) geometric averaging of two independent SS models for global DD records. Findings: The detected self-similar recurrences in the global response suggest three global self-similar waves that support multi-month forecasts of the DD numbers. However, there are upper and lower-limit SS forecast DD scenarios that were jointly integrated with a geometrical average (GA) model, that support the existence of a moderated third wave, with a decaying stage for the next months (July-September 2020). It appears that the third world (South America [SAM]+Asia [ASI] +Africa [AFR]), is the actual big player, (following China, and Europe [EUR]+North America [NAM]) with its biggest contribution to a global third wave (W3) of C19P. Conclusion: The empirical global modeling of the C19P has suggested us a possible moderated W3 scenario, with contributions mainly coming from the third world people. This moderated W3 scenario, after to be calibrated with the last weeks, has provided to stakeholders of significant data and criteria to define, sustain and support plans for the next months, based on data and self-similarities. These scenarios provide a well-based perspective on non-linear dynamics of C19P, that will complement the standard health and economic models.
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