Coronavirus disease 2019 (COVID-19) has placed stress on all National Health Systems (NHSs) worldwide. Recent studies on the disease have evaluated different variables, namely, quarantine models, mitigation efforts, damage to mental health, mortality of the population with chronic diseases, diagnosis, use of masks and social distancing, and mortality based on age. This study focused on the four NHSs recognized by the WHO. These systems are as follows: (1) The Beveridge model, (2) the Bismarck model, (3) the National Health Insurance (NHI) model, and (4) the “Out-of-Pocket” model. The study analyzes the response of the health systems to the pandemic by comparing the time in days required to double the number of disease-related deaths. The statistical analysis was limited to 56 countries representing 70% of the global population. Each country was grouped into the health system defined by the WHO. The study compared the median death toll DT, between health systems using Mood's median test method. The results show high variability of the temporal trends in each group; none of the health systems for the three analyzed periods maintain stable interquartile ranges (IQRs). Nevertheless, the results obtained show similar medians between the study groups. The COVID-19 pandemic saturates health systems regardless of their management structures, and the result measured with the time for doubling death rate variable is similar among the four NHSs.