If your goal is to stop mutations from happening, yes, you need everyone in the world to go on full lockdown for 4 weeks. And then test everybody and quarantine

If your goal is to stop mutations from happening, yes, you need everyone in the world to go on full lockdown for 4 weeks. And then test everybody and quarantine until the disease is gone. The situation right now is that you have plenty of breeding grounds for new mutations, and it only needs some minor crossing of borders for these to get through. I would also say it's infeasible for non-island nations that need to trade with other countries to completely lock the borders.