  To curb the spread of COVID-19, many governments around the world have
implemented tiered lockdowns with varying degrees of stringency. Lockdown
levels are typically increased when the disease spreads and reduced when the
disease abates. A predictive control approach is used to develop optimized
lockdown strategies for curbing the spread of COVID-19. The strategies are then
applied to South African data. The South African case is of interest as the
South African government has defined five distinct levels of lockdown, which
serves as a discrete control input. An epidemiological model for the spread of
COVID-19 in South Africa was previously developed, and is used in conjunction
with a hybrid model predictive controller to optimize lockdown management under
different policy scenarios. Scenarios considered include how to flatten the
curve to a level that the healthcare system can cope with, how to balance lives
and livelihoods, and what impact the compliance of the population to the
lockdown measures has on the spread of COVID-19. The main purpose of this paper
is to show what the optimal lockdown level should be given the policy that is
in place, as determined by the closed-loop feedback controller.
