Application of optimal control to the dynamics of COVID-19 disease in South Africa

Abstract

SARS-CoV-2 (COVID-19) belongs to the beta-coronavirus family, which include: the severe acute respiratory syndrome coronavirus (SARS-CoV) and the Middle East respiratory syndrome coronavirus (MERS-CoV). Since its outbreak in South Africa in March 2020, it has lead to high mortality and thousands of people contracting the virus. Mathematical analysis of a model without controls was done and the basic reproduction number (R0) of the COVID-19 for the South African pandemic determined. Permissible controls were introduced and an optimal control problem using the Pontraygain Maximum Principle is formulated. Numerical findings suggest that joint implementation of effective mask usage, physical distancing and active screening and testing, are effective measures to curtail the spread of the disease in the human population. The results obtained in this paper are of public health importance in the control and management of the spread for the novel coronavirus, SARS-CoV-2, in South Africa.

Keywords

• COVID-19
• South Africa
• Optimal control measures
• Constant control
• Model fitting
• Numerical simulations