Fig. 2

Weak intervention with large \(R_{0,\mathrm{on}}=1.4>1\). Parameters are \(\beta _{\mathrm{off}}=2/7 \ \mathrm{days}^{-1}\) and \(\gamma =1/7 \ \mathrm{days}^{-1}\). A Time series of the fraction of infected and removed individuals, i(t) in blue and r(t) in orange, without the intervention. Time series with the intervention with \(\beta _{\mathrm{on}}=1.4/7 \ \mathrm{days}^{-1}\) and the intervention duration, \(\Delta t=60\) days, with onset times B \(t_{\mathrm{on}}= 10\) days, C \(t_{\mathrm{on}}= 19.2\) days, D \(t_{\mathrm{on}}=33.4\) days, and E \(t_{\mathrm{on}}=65\) days, are depicted. The intervention is implemented for \(t_{\mathrm{on}}\le t \le t_{\mathrm{off}}=t_{\mathrm{on}}+\Delta t\) and are represented by grey intervals in these panels. Conditions for the peaks of the fraction of infected individuals are given by \(s(t)=1/R_{0,\mathrm{off}}\), when the intervention is not implemented, and by \(s(t)=1/R_{0,\mathrm{on}}\) during intervention. The final size of the outbreak for each case is represented by \(r(\infty )\). F and G represent the maximum fraction of infected individuals \(i_{\mathrm{max}}\) normalized by that without the intervention \(i_\mathrm{max}^0\), plotted in terms of \(r(t_{\mathrm{on}})\) and \(\Delta r = r(t_{\mathrm{off}})-r(t_{\mathrm{on}})\), and \(t_{\mathrm{on}}\) and \(\Delta t\), respectively. Symbols A–E in F and G denote the intervention timings of the time series of the corresponding in A–E. Symbols (i)-(iv) in F denote the timing that the maximum infected fraction is observed, as described in the main text. The boundaries between regions shown in F are obtained analytically. See the main text for the details