Convergence of FPSP policies and .

(Top) Time-behaviour of a 7-days FPSP policy with [X, Y] = [1, 6] with a single workday followed by six days lockdown. In the first 20 days (see the vertical orange dashed line) the virus invades a totally susceptible population generating a major epidemic with reproductive number . From the end of week 3 to the end of week 6 a major lockdown is enforced reducing the reproductive number to . The FPSP is initiated in week 7 (see the vertical dashed light blue line). The epidemic has a trajectory that approximates that of a system with average . (Bottom) Time-behaviours generated by five FPSPs of increasing frequency (corresponding to periods T ranging from 5 to 1 weeks) and the same duty-cycle DC = 1/7 = 2/14 = 3/21 = 4/28 = 5/35 ≃ 14.3%. In all cases, the epidemic behaviour seen in the first three weeks is suppressed and the outbreak dies out following closely the trajectory of an un-switched system with (dashed blue line). As clearly show in the figure, smaller periods are associated with a higher vicinity to the average trajectory (dashed blue line).