[Mathematical models for COVID-19 infection estimation: essential considerations and projections in Colombia].

Objective: To estimate the COVID-19 infection behavior in Colombia using mathematical models.

Methods: Two mathematical models were constructed to estimate imported confirmed cases and related confirmed cases of COVID-19 infection in Colombia, respectively. The phenomenology of imported confirmed cases is modeled with sigmoidal function, while related confirmed cases are modeled using a combination of exponential functions and polynomial algebraic functions. The fitting algorithms based on least squares methods and direct search methods are used to determine the parameters of the models.

Results: The sigmodial model performs a highly convergent estimation of the reported confirmed cases of COVID-19 infection to May 28, 2020. This model achieved a prediction error of 0.5 % measured using the normalized root mean square error. The model of the confirmed cases reported as related shows a 3.5 % prediction error and a low bias of -0.01 associated with overestimation.

Conclusions: This work shows that the mathematical models allow to predict the behavior of the infection efficiently and effectively by COVID 19 in Colombia when the imported cases and the related cases of infection are independently considered.