Control systems with high lag like this are incredibly difficult to work with. Especially in the presence of exponential growth like this system has—if you accidentally let R get a bit too high, it will be a week or two before you notice, and in that time you will have seeded a ton of cases that you will have to track down and deal with.
This is why you need to have borders on multiple scales and cancellation of large events.
If one case slips through, in a week or two they will infect a handful of new people. If you have set up a system of regional and national borders, as well as cancelled large events, you will find out about this trace the contacts and temporarily increase the strength of the lockdown in only that region.
This strategy nearly worked in South Korea, but then patient 31 was a superspreader:
This is why you need to have borders on multiple scales and cancellation of large events.
If one case slips through, in a week or two they will infect a handful of new people. If you have set up a system of regional and national borders, as well as cancelled large events, you will find out about this trace the contacts and temporarily increase the strength of the lockdown in only that region.
This strategy nearly worked in South Korea, but then patient 31 was a superspreader:
https://graphics.reuters.com/CHINA-HEALTH-SOUTHKOREA-CLUSTERS/0100B5G33SB/index.html