In the absence of vaccines and effective antiviral drugs, control of the spread of coronavirus disease (Covid-19) relies mainly on the adequacy of public health resources and policies. Hence, failure to establish and implement scientifically reliable control measures may have a significant effect on the incidence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, severity of the disease, and death toll. The average number of secondary transmissions from an infected person, or reproduction numbers (R0 and R), and the points at which the collective immunity begins to reduce the transmission of the infection, or herd immunity thresholds, are important epidemiological tools used in strategies of Covid-19 control, suppression, and mitigation. However, SARS-CoV-2 transmission through asymptomatic carriers and, possibly, aerosols, has been ignored, and this may affect the effectiveness of Covid-19 control strategies. Therefore, consideration of the two possible ways of transmission would substantially increase the values of reproduction numbers, but if estimates of the contingent of the population naturally resistant to the virus, plus those with pre-existing cross-immunity to SARS-CoV-2 were considered, the evaluation of herd immunity thresholds should reach their real and achievable levels.