Systematic description of COVID-19 pandemic using exact SIR solutions and Gumbel distributions Amaro Soriano, José Enrique COVID-19 coronavirus SIR model Differential equations Gumbel distribution An epidemiological study is carried out in several countries analyzing the first wave of the COVID-19 pandemic using the SIR model and Gumbel distribution. The equations of the SIR model are solved exactly using the proper time as a parameter. The physical time is obtained by integration of the inverse of the infected function over proper time. Some properties of the solutions of the SIR model are studied such as time scaling and the asymmetry, which allows to obtain the basic reproduction number from the data. Approximations to the solutions of the SIR model are studied using Gumbel distributions by least squares fit or by adjusting the maximum of the infected function. Finally, the parameters of the SIR model and the Gumbel function are extracted from the death data and compared for the different countries. It is found that ten of the selected countries are very well described by the solutions of the SIR model, with a basic reproduction number between 3 and 8. 2023-01-23T13:12:45Z 2023-01-23T13:12:45Z 2022-09-29 info:eu-repo/semantics/article Amaro, J.E. Systematic description of COVID-19 pandemic using exact SIR solutions and Gumbel distributions. Nonlinear Dyn 111, 1947–1969 (2023). [https://doi.org/10.1007/s11071-022-07907-4] https://hdl.handle.net/10481/79270 10.1007/s11071-022-07907-4 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Springer