Before revision:  Using epidemiological data from Germany, we show that NPIs reduced non-local contacts in the transmission network, resulting in a change from an exponential to a constant regime . Due to the small-world nature of the inferred network, exponential spread can be efficiently prevented by reducing non-local contacts. Eliminating the disease remains costly as it requires to reduce all contacts. Our code is freely available and can be readily adapted to any country .
After revision:  Using epidemiological data from Germany, we show that NPIs reduced non-local contacts in the transmission network, resulting in a change from an exponential to a constant regime of newcases. In this regime, the disease spreads like a wave with a finite wave speed that depends on the number of contacts in a nonlinear fashion, which we can predict by mean field theory. Our analysis indicates that besides the well-known transitionbetween exponential increase and exponential decrease in the number of new cases, NPIs can induce a transition to another, previously unappreciated regime of constant new cases .