A Novel Metaheuristic Framework Based on the Generalized Boltzmann Distribution for COVID-19 Spread Characterization

Coronavirus disease 2019 (COVID-19) is a highly communicable viral infection caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2), which has spread rapidly throughout the world. From a computer science point of view, research efforts have focused on the use of approaches such as machine learning and curve fitting to predict or simulate disease behavior. However, the mathematical characterization of the spread of COVID-19 is a topic that has not yet been explored by these techniques. In this work, we propose a novel metaheuristic framework called META-COVID19, which merges the Generalized Boltzmann distribution and the family of Jacobi polynomials to automatically characterize the COVID-19 spread without prior knowledge of the data and without involving a human expert. In general terms, the algorithm receives as input a time series of daily reported cases and the output is a polynomial mathematical model. Our framework only needs a single parameter, which is the number of Jacobi polynomials to analyze during the iterative process, and it is capable of proposing polynomials whose adjustment error is close to 1E-3. Finally, we show the applicability of the polynomial models found by META-COVID19, through a theoretical mathematical analysis in order to know attributes of the spread of COVID-19 in different periods of time, allowing to generate better strategies to face it in the future.