Introduction The novel Coronavirus disease (COVID-19), caused by the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), in Africa is characterised by a more substantial proportion of asymptomatic (or mildly symptomatic) individuals thought to be playing a role in the spread of the infection. The exact proportion and degree of infectiousness of asymptomatic individuals remains unclear. Studies however indicate that their management is crucial for control of SARS-CoV-2 transmission. Methodology We developed a simplified deterministic susceptible-exposed-infectious-removed (SEIR) mathematical model to assess the effect of active isolation of SARS-CoV-2 infected but asymptomatic individuals through blanket testing for control of the outbreak in Lusaka Province of Zambia. Here we modelled two scenarios; (1) assuming asymptomatic individuals comprised 70% of all COVID-19 cases and (2) asymptomatic individuals comprised only 50% of the cases. For contrast, the model was assessed first under the assumption that asymptomatic individuals are equally as infectious as symptomatic individuals and then secondly, and more likely, assuming asymptomatic individuals are only half as infectious as symptomatic individuals. Results For the model assuming 70% asymptomatic cases, a minimum sustained daily blanket testing rate of [greater than or equal to] 7911 tests/100000 population was sufficient to control the outbreak if asymptomatic individuals are only half as infectious while if equal infectiousness was assumed then a testing rate of [greater than or equal to] 10028 tests/ 100000 population would be required. For 50% asymptomatic, minimum blanket testing rates of [greater than or equal to] 4540 tests/ 100000 population was sufficient to control the outbreak at both assumed levels of infectiousness for asymptomatic individuals relative to symptomatic individuals. Discussion and conclusion Our model predicts that active isolation of COVID-19 cases, including asymptomatic individuals, through blanket testing can be used as a possible measure for the control of the SARS-Cov-2 transmission in Lusaka, Zambia, but it would come at a high cost.