Applied Mathematics & Information Sciences

Author Country (or Countries)

South Africa


The unexpected continuing mushrooming tendency of the COVID-19 epidemic calls for alarm in the entire globe especially with the cropping up of more divergent contagious variants being witnessed. On top of the many non-pharmaceutical measures put in place for containment of the pandemic, pharmacological measures have been incorporated in the battle against the SARS-CoV-2 especially with the commencement of vaccination in the early December 2020. This study develops a deterministic compartmental model that incorporates vaccination as a measure to combat the spread of COVID-19 epidemic. We use the model particularly to assess the potential impact of vaccination in shattering the chain of transmission of the virus in South Africa. Verification of the model is carried out by performing its best fit to cumulative COVID-19 positive cases data as reported by the government of the Republic of South Africa utilizing the maximum likelihood estimation algorithm implemented in fitR package. With some vaccines already being under utility while other are being developed, we consider two major vaccine efficacy scenarios. One scenario accounts for general hypothetical vaccines with 20%,50%,65% and 85% case efficacy. The other scenario considers the Johnson and Johnson’s Janssen vaccine with its distinctive efficacy levels as reported to act against the 501Y.V2 variant. The sensitivity analysis and simulations for the model reveal that the cumulative infections decline drastically with increased extent of vaccination at each level of the vaccine efficacy. The study fundamentally discovers that vaccinating approximately 20% of the population with a vaccine of at least 60% efficacy would be sufficient in elimination of the pandemic over relatively shorter time. Moreover, with J&J vaccine maintaining its efficacious level against the 501Y.V2 variant, it would be the best vaccine to shortly eradicate the COVID-19 epidemic in South Africa.

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