  The traditional long-term solutions for epidemic control involve eradication
or population immunity. Here, we analytically derive the existence of a third
viable solution: a stable equilibrium at low case numbers, where
test-trace-and-isolate policies partially compensate for local spreading
events, and only moderate restrictions remain necessary. In this equilibrium,
daily cases stabilize around ten new infections per million people or less.
However, stability is endangered if restrictions are relaxed or case numbers
grow too high. The latter destabilization marks a tipping point beyond which
the spread self-accelerates. We show that a lockdown can reestablish control
and that recurring lockdowns are not necessary given sustained, moderate
contact reduction. We illustrate how this strategy profits from vaccination and
helps mitigate variants of concern. This strategy reduces cumulative cases (and
fatalities) 4x more than strategies that only avoid hospital collapse. In the
long term, immunization, large-scale testing, and international coordination
will further facilitate control.
