Fig. 2

Value of X giving the minimum value of Eq. (12), as a function of Y and \(\lambda\), based on numerical simulation of the cloSIR model. A clear transition from \(X = 0\) (yellow) to \(X=1\) (blue) is seen, with no intermediary values. The solid black line corresponds to the theoretical closed-form solution from Eq. (13), while the dashed grey line corresponds to the rough approximation \(Y > 1 - e^{-\lambda }\) past which it is best to not have any closures