question: We present results on the existence of various common patterns in the growth of the total number of patients affected by COVID-19, a disease acquired through infection by a novel coronavirus, in different countries. For this purpose we propose a scaling model that can have general applicability in the understanding of real data of epidemics. This is analogous to the finite-size scaling, a technique used in the literature of phase transition to identify universality classes. In the disease model, the size of a system is proportional to the volume of the population, within a geographical region, that have been infected at the death of the epidemic or are eventually going to be infected when an epidemic ends. Outcome of our study, for COVID-19, via application of this model, suggests that in most of the countries, after the `onset' of spread, the growths are described by rapid exponential function, for significantly long periods. In addition to accurately identifying this superuniversal feature, we point out that the model is helpful in grouping countries into universality classes, based on the late time behavior, characterized by physical distancing practices, in a natural way. This feature of the model can provide direct comparative understanding of the effectiveness of lockdown-like social measures adopted in different places.