Application of Optimal Control to Long Term Dynamics of COVID-19 Disease in South Africa

Nyabadza, Farai; Chukwu, Williams; Chirove, Faraimunashe; fatmawati, fatmawati; Gatyeni, Princess

SARS-CoV-2 (COVID-19) belongs to the beta-coronavirus family, these include; the severe acute respiratory syndrome coronavirus (SARS-CoV) and the Middle East respiratory syndrome coronavirus (MERS-CoV). Since its resurgence in South Africa in March 2020, it has lead to high mortality and thousands of people contracting the virus. In this study, we use a set of five differential equations to analyse the effects on long term dynamics of COVID-19 pandemic with optimal control measures. Mathematical analyses of the model without control were done and the basic reproduction number (R0) of the COVID-19 for the South African epidemic determined. The model steady states were also determined, and their analyses presented based on R0: We introduced permissible control measures and formulated an optimal control problem using the Pontraygain Maximum Principle. Our 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 on undiagnosed humans. 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.