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The coronavirus disease 2019 (COVID-19) epidemic was investigated within a general Susceptible-Infectious-Removed (SIR) model, especially the distributions of its dead cases and infectious ones. This paper applied its nonextensive modification with respect to more realistic situations. A time-dependent SIR model was modified when particularly regarding control and mitigation measures in response to the societal impacts of epidemics and pandemics. We validated all the theoretical results by fitting the derived q -distributions with data from the COVID-19 pandemic in the world. It was found that not all the changeable fit parameters are independent, some of which shared common properties, a result corroborated by our model prediction. Our modified SIR model was proved to be effective in fitting the COVID-19 epidemic distributions. The relative non-extensive parameter was strongly connected with the freedom of systems, which thus threw a light upon the prevention and treatment of disease next in the world.