Fig 4. Influence of heterogeneities in transmission.

We investigate how differences in transmissibility among groups (e.g., due to demographic or spatial factors) fundamentally limit the ability to detect resurgence from a specific group (in this example group 1 with reproduction number R_s[1]). Panel A shows that the grouped posterior distribution becomes less sensitive to a fixed relative change in group 1 incidence, ${\Delta \lambda }_{\tau \left(s\right)}\left[1\right]=\frac{i_{\tau \left(s\right)}\left[1\right]-{\lambda }_{\tau \left(s\right)}\left[1\right]}{{\lambda }_{\tau \left(s\right)}\left[1\right]}$ (the level of change increases from blue to red). Posterior distributions over ${\overline{R}}_s$ (the overall reproduction number across groups) are more overlapped (and tighter in variance) as p rises, for fixed R_s[1] (top). Panel B plots how overall resurgence detection probability $\mathrm{P}\left({\overline{R}}_s>1\right)$ depends on the weight (α₁, top, 0.05–1) and epidemic size (λ_τ(s)[1], middle, 20–80, p = 2) as well as changes in R_s[3] (bottom, 0.5–1.2, p = 3). Decreases in α₁ (red to blue) or λ_τ(s)[1] mean other groups mask the resurging dynamics in group 1, reducing sensitivity (curves become less steep). In the latter case the $P\left({\overline{R}}_s>1\right)$ (green with solid line at median of λ_τ(s)[1] range) is always more conservative than P(R_s[1]>1) (black with solid median line). As R_s[3] falls (red to blue) the ability to detect resurgence also lags relative to that from observing group 1 (black).