Figure 3.

Accuracy and relative error of the peak total prevalence approximated using the formula for the basic SIR model (equation (4.22)), as a function of the probability that an infection is mild ($m$). Parameters other than $m$ are set to the values specified in tables 2 and 3. For each $m$, the value of ${\mathcal{R}}_0$ is computed using equation (4.1). The relative error is $\frac{\mathtt{S}\mathtt{I}\mathtt{R}-\mathtt{T}\mathtt{R}\mathtt{U}\mathtt{E}}{\mathtt{T}\mathtt{R}\mathtt{U}\mathtt{E}}$, where TRUE refers to the peak total prevalence obtained by numerically solving equation (3.1), and SIR refers to equation (4.22). The maximum relative error of the approximation is 5.5%, for $m=0.7$ (${\mathcal{R}}_0=3.12$). In the extreme of perfect variolation ($m=1$), ${\mathcal{R}}_0={\mathcal{R}}_{0,\mathrm{m}}=2.02$, whereas in the extreme of completely ineffective variolation ($m=0$), ${\mathcal{R}}_0={\mathcal{R}}_{0,\mathrm{s}}=5.69$.