This paper provides an estimation of the accumulated detection rates and the accumulated number of infected individuals by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Worldwide, on July 20, it has been estimated above 160 million individuals infected by SARS-CoV-2. Moreover, it is found that only about 1 out of 11 infected individuals are detected. In an information context in which population-based seroepidemiological studies are not frequently available, this study shows a parsimonious alternative to provide estimates of the number of SARS-CoV-2 infected individuals. By comparing our estimates with those provided by the population-based seroepidemiological ENE-COVID study in Spain, we confirm the utility of our approach. Then, using a cross-country regression, we investigated if differences in detection rates are associated with differences in the cumulative number of deaths. The hypothesis investigated in this study is that higher levels of detection of SARS-CoV-2 infections can reduce the risk exposure of the susceptible population with a relatively higher risk of death. Our results show that, on average, detecting 5 instead of 35 percent of the infections is associated with multiplying the number of deaths by a factor of about 6. Using this result, we estimated that 120 days after the pandemic outbreak, if the US would have tested with the same intensity as South Korea, about 85,000 out of their 126,000 reported deaths could have been avoided.