Cases, deaths and wastewater are all delayed, scaled views of the same infections. If one stream's scaling drifts — say a rising death-to-infection ratio — it starts to imply a different trajectory than the others. A joint model that assumes constant scaling cannot satisfy both, so it settles on a compromise that fits none of them. Drag the drift up to create the conflict, then let the scaling vary to resolve it.
One shared epidemic, several lenses
Each stream implies its own answer to "what did the infections do?"
Every stream is the shared latent infections passed through its own scaling. Invert that scaling and each stream implies an infection trajectory. When the scalings are what the model assumes, the implied trajectories agree and pinning down infections is easy. When one scaling drifts, its implied trajectory peels away from the rest, and the streams conflict.
Here cases and wastewater keep a constant scaling, so both imply the true trajectory. Only the death scaling (the infection fatality ratio) drifts upward over the second half of the outbreak, so the deaths imply a trajectory that keeps rising when the truth is falling.
Conflict, and how to resolve it
Raise the drift to open a gap; let the scaling vary to close it
Schematic illustration, not a real posterior: the estimate is a simple weighted blend of the implied trajectories, drawn to show the intuition rather than the output of fitting the Stan model.
death scaling by end = —× its startestimate error vs truth = —
The point. With a constant-scaling model the estimate is dragged toward a compromise between the trajectory the cases/wastewater imply and the (wrong) one the deaths imply. It fits neither stream, and the error grows with the drift. Sharing one infection process surfaces the conflict but does not resolve it. Letting the death scaling vary models the reason the streams disagree, so the estimate snaps back onto the truth.
Takeaways
Streams conflict when their implied infection trajectories are incompatible — here a drifting death scaling makes the deaths imply a rising epidemic while the cases and wastewater imply a falling one.
A joint model with a constant scaling settles on a compromise that is faithful to no stream, and the miss grows with the drift.
Sharing one latent infection process surfaces the conflict; it does not resolve it.
You resolve genuine conflict by modelling the reason for it — here, letting the death scaling vary over time — not by averaging the streams together.