We have developed a nonlinear method of time series analysis that allows us to obtain multiple nonlinear trends without harmonics from a given set of numerical data. We propose to apply the method to recognize the ongoing status of COVID-19 infection with an analytical equation for nonlinear trends. We found that there is only a single nonlinear trend, and this result justifies the use of a week-based infection growth rate. In addition, the fit with the obtained analytical equation for the nonlinear trend holds for a duration of more than three months for the Delta variant infection time series. The fitting also visualizes the transition to the Omicron variant.