The SIR model and its variants are widely used to predict the progress of COVID-19 worldwide, despite their rather simplistic nature. Nevertheless, robust estimation of the SIR model presents a significant challenge, particularly with limited and possibly noisy data in the initial phase of the pandemic. K-means algorithm is used to perform a cluster analysis of the top ten countries with the highest number of COVID-19 cases, in order to observe if there are any significant differences among countries in terms of robustness. As a result of model variation tests, the robustness of parameter estimates is found to be particularly problematic in developing countries. The incompatibility of parameter estimates with the observed characteristics of COVID-19 is another potential problem. Hence, a series of research questions are visited. We propose an SPE (“Single Parameter Estimation”) approach to circumvent these potential problems if the basic SIR is the model of choice, and we check the robustness of this new approach by model variation and structured permutation tests. Dissemination of quality predictions is critical for policy and decision-makers in shedding light on the next phases of the pandemic.