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• Two contrasting models are presented to understand and predict the spreading of COVID-19. • Estimation of turnaround (peak active cases) day is performed using a mathematical model for India, Italy and USA. • Trend and variability are extracted from the data for daily reported cases using DCT-based Fourier decomposition method. • Bi-modal Gaussian mixture model is fitted to the trend to predict the cases in near future. • End-dates for COVID-19 are predicted with 95% confidence interval in various parts of the world. COVID-19 is caused by a novel coronavirus and has played havoc on many countries across the globe. A majority of the world population is now living in a restricted environment for more than a month with minimal economic activities, to prevent exposure to this highly infectious disease. Medical professionals are going through a stressful period while trying to save the larger population. In this paper, we develop two different models to capture the trend of a number of cases and also predict the cases in the days to come, so that appropriate preparations can be made to fight this disease. The first one is a mathematical model accounting for various parameters relating to the spread of the virus, while the second one is a non-parametric model based on the Fourier decomposition method (FDM), fitted on the available data. The study is performed for various countries, but detailed results are provided for the India, Italy, and United States of America (USA). The turnaround dates for the trend of infected cases are estimated. The end-dates are also predicted and are found to agree well with a very popular study based on the classic susceptible-infected-recovered (SIR) model. Worldwide, the total number of expected cases and deaths are 12.7 × 106 and 5.27 × 105, respectively, predicted with data as of 06-06-2020 and 95% confidence intervals. The proposed study produces promising results with the potential to serve as a good complement to existing methods for continuous predictive monitoring of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]