Add latent infection process "SharedInfection"

[cdc-mitzimorris]

PyRenew's multi-signal model framework currently has one latent infection process: HierarchicalInfections, which decomposes $\mathcal{R}(t)$ into a baseline plus per-subpopulation deviations. This is the right tool when observation processes operate at different spatial resolutions (e.g., jurisdiction-level hospital admissions + site-level wastewater concentrations), as demonstrated in building_multisignal_models.qmd.

However, a common use case has no subpopulation structure: two jurisdiction-level aggregate signals (e.g., hospital admissions + ED visits) observe the same underlying infection process through different delay distributions and ascertainment rates. Using HierarchicalInfections with subpop_fractions=[1.0] for this case is misspecified: the deviation process samples ~N nuisance parameters (one per timepoint) that are all forced to zero by the sum-to-zero constraint. This creates serious non-identifiability.

Add class SharedInfecions with a single $\mathcal{R}(t)$ trajectory that drives one renewal equation. Multiple observation processes observe the resulting aggregate infection trajectory through their own ascertainment rates and delay distributions.

Mathematical form:

• $\log \mathcal{R}(t) \sim \text{TemporalProcess}$ (e.g., AR(1), RandomWalk)
• $I(t) = \mathcal{R}(t) \sum_\tau I(t-\tau) , g(\tau)$
• Each observation: $\mu_k(t) = \alpha_k \sum_s I(t-s) , \pi_k(s)$