After the quarantine/isolation/stay-at-home orders stop, will the disease stop spreading?
Absolutely not. There will be second waves of the disease even in countries that have effectively suppressed the first round. Two of these countries are Taiwan and Singapore who have experienced previous outbreaks from China, including SARS. They effectively quarantined sick people, isolated and ordered stay-at-home. They shuttered their economies used tracing methods and systematic tracking techniques. These have worked effectively but the virus is still in the general population particularly in asymptomatic infected people. They will spread the disease and symptomatic cases will occur again. This is going to happen in America. There will be a more severe round in multiple waves of the disease as we have not followed the same rigid even contact tracing, tracking, rigid isolation, extensive testing of symptomatic and asymptomatic patients along with other draconian measures. There will be waves of this as the virus runs its course. Two factors that will affect this are herd immunity and the development of the vaccine.
It is interesting to note that the Spanish flu 1918 was noted to still be in circulation and an active source of infection albeit in relatively low numbers through 2009 when the new version of H1N1 arrived.
There will be reservoirs of the virus in third world nations and densely populated areas. While the first world may be able to help mitigate and control this unless the Middle East, sub-Sahara Africa, Malaysia, Indonesia and India can control this virus will continue to re-infect the rest of the world until a vaccine. If the virus can hang around long enough it can mutate. We have experience with this. This occurred with the Spanish flu when a new strain developed a year after the original strain in 1919 and re-infecting the world.