Long-term epidemic dynamics with time-dependent contact rate. (A, B) Contact rate reduced in response to the surge in the daily number of cases. (C) Contact rate reduced in response to the surge in the daily number of cases and modulated by the duration of the quarantine. In panels A and C, initial θ = 1.14, which is equal to last-week θ for Italy. In all panels, population size N = 50 million and R(t = 0) = 500.