Precise extrapolative mining and analysis of relevant dataset during or after any disease outbreak can assist the government, stake holders and relevant agencies in the health sector to make important decisions with respect to the disease outbreak control and management. While prior works has concentrated on non-stationary long term data, this work focuses on a short term non-stationary and relatively noisy data. Particularly, a distinctive nonparametric machine learning method based kernel-controlled probabilistic Gaussian process regression model has been proposed and employed to model and analyze Covid-19 pandemic data acquired over a period of approximately six weeks. To accomplish the aim, the MATLAB 2018a computational and machine learning environment was engaged to develop and perform the Gaussian process extrapolative analysis. The results displayed high scalability and optimal performance over the commonly used machine learning methods such as the Neural networks, Neural-Fuzzy networks, Random forest, Regression tree, Support Vector machines, K-nearest neighbor and Discriminant linear regression models. These results offer a solid foundation for conducting research on reliable prognostic estimations and analysis of contagious disease emergence intensity and spread.