Country reported case counts suggested a slow spread of SARS-CoV-2 in the initial phase of the COVID-19 pandemic in Africa. However, due to inadequate public awareness, unestablished monitoring practices, limited testing, ineffective diagnosis, stigmas attached to being infected with SARS-CoV-2, self-medication, and the use of complementary/alternative medicine that are common among Africans for social, economic, and psychological reasons, there might exist extensive under-ascertainment and therefore an underestimation of the true number of cases, especially at the beginning of the novel epidemic. We developed a compartmentalized epidemiological model based on an augmented susceptible-exposed-infectious-recovered (SEIR) model to track the early epidemics in 54 African countries. Data on the reported cumulative number of cases and daily confirmed cases were used to fit the model for the time period with no or little massive national interventions yet in each country. We estimated that the mean basic reproduction number is 2.02 (SD 0.7), with a range between 1.12 (Zambia) and 3.64 (Nigeria), whereas the mean basic reproduction number for observed cases was estimated to be 0.17 (SD 0.17), with a range between 0 (Sao Tomé and Príncipe, Seychelles, Tanzania, South Sudan, Mozambique, Liberia, Togo) and 0.68 (South Africa). It was estimated that the mean overall report rate is 5.37% (SD 5.71%), with the highest 30.41% in Libya and the lowest 0.02% in Sao Tomé and Príncipe. An average of 5.46% (SD 6.4%) of all infected cases were severe cases and 66.74% (SD 17.28%) were asymptomatic ones, with Libya having the most (39.45%) fraction of severe cases and Togo the most (97.38%) fraction of asymptomatic cases. The estimated low reporting rates in Africa suggested a clear need for improved reporting and surveillance system in these countries.