Fig. 3.

Conditions for outbreak prevention via${\mathcal{R}}_0$analysis. (left) Basic reproduction number ${\mathcal{R}}_0$ for $S^{\ast }=1$ and $u_n=0$ as a function of adoption fraction $u_a$ and social interventions $u_s$. The dashed curve shows the ${\mathcal{R}}_0=1$ level set, which is the intervention threshold separating an outbreak from no outbreak. Increasing social intervention $u_s$ or contact tracing adoption $u_a$ increases disease control. (right) Intervention thresholds for $S^{\ast }\in \{1,0.925,0.85,0.775,0.7\}$ and $u_n=0$. Dotted curves show the level sets ${\mathcal{R}}_0{|}_{S^{\ast }=1}{S}^{\ast }=1$ and correspond to neglecting the dependence of the contact tracing efficiency on $S^{\ast }$. Previous contact tracing descriptions do not account for the susceptible proportion of the population, and thus underestimate the necessary disease control.