[jltsiren]

There is a similar justified mechanical model with vaccinations. A toy version is that vaccinated people are X% less likely to get infected and Y% less effective at spreading the disease if they get infected. If compliance with vaccination policies and other mitigation measures is at least Z%, then the outbreak will be contained before most people get infected.

With novel diseases, it's usually impossible to have accurate enough estimates of the numerical parameters in advance to determine if lockdowns and vaccine mandates are going to work. And the compliance rate is fundamentally political. A few key individuals, such as politicians and judges, can have an outsized effect on it. Containment that would have worked otherwise may fail due to the actions of those individuals.