Route-decomposed Cori effective reproductive number from ensemble trajectories

Computes the per-location, time-varying Cori (2013) instantaneous infection reproductive number split by transmission route, $R^{\mathrm{eff}}_{jt} = R^{\mathrm{hum}}_{jt} + R^{\mathrm{env}}_{jt}$, by an analytic reduction over the ensemble trajectories the run already captured (no extra simulation).

Usage

calc_Reff(
  ensemble,
  config,
  weights = NULL,
  probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
  infectiousness_floor = 1,
  verbose = TRUE
)

Arguments

ensemble: A mosaic_trajectories artifact (2_calibration/trajectories_ensemble.rds) or a mosaic_ensemble carrying one in $trajectories. Must provide weighted-median incidence_human and incidence_env channels; E, Isym and Iasym supply the initial infectious stocks.
config: The medoid config list: kernel parameters iota, gamma_1, gamma_2, sigma, zeta_1, zeta_2, plus the fields the engine needs to rebuild $\delta_{jt}$ (psi_jt, decay_*).
weights: Optional per-member weights for the posterior reduction, indexed by member id. NULL (default) uses the weights in lines.
probs: Credible-interval quantile probabilities.
infectiousness_floor: Numeric scalar $\ge 0$. Minimum route infectiousness (effective past infections) required to report that route's R at a step (a route below it with no infections of its own contributes 0 to the total). Default 1; 0 is the pure Cori convention.
verbose: Logical; emit progress messages.

Value

A tidy long data.frame (reproductive_numbers schema): location, date, t, estimand ("R_eff", "R_hum", "R_env"), central (renewal on the weighted-median route incidences) and one column per quantile. Attributes: central_matrix (R_eff, nL x T), route_central (list of R_hum and R_env matrices), env_share, kernel ("route_instantaneous"), kernel_params, ci_source, caveat.

Details

Estimand. Each route's numerator is its own infection incidence (incidence_human, incidence_env); both denominators are driven by total incidence, because every infection is infectious through both routes. $\Lambda^{hum}$ propagates past infections through the latent and infectious states (symptomatic and asymptomatic at equal weight, as in the human force of infection). $\Lambda^{env}$ additionally routes their shedding (weighted by zeta_1, zeta_2) through the reservoir, which decays at the $\psi$-dependent rate $\delta_{jt}$, so the environmental generation interval (tens to hundreds of days) and its seasonal variation are represented. Both kernels are derived from the engine's own daily transition probabilities and phase order. The estimate is instantaneous: the reservoir is built from the actual past decay path and one infection's lifetime reservoir contribution is evaluated at today's $\delta_{jt}$ (secondary infections per infection if conditions stayed as they are at t). Nothing after t enters, so truncating the series does not change earlier values. WASH (theta_j), the absolute shedding scale, kappa and the transmission rates cancel from the kernels and live in the R values.

Initial conditions. People already latent or infectious at the start (the E, Isym, Iasym stocks on the first day) are included in both infectiousness terms, so the series is defined from the start. R in roughly the first $1/\delta$ days still reflects the reservoir filling from empty and is best read after a burn-in (add_reproductive_numbers() applies one).

Caveat. This describes the simulated trajectory (comparable to a surveillance-derived R_eff computed the same way); it is not an invasion threshold. The renewal assumes transmission is linear in infectiousness; the human FOI uses $I^{\alpha_1}$ and the environmental dose saturates, so both route values are trajectory descriptors, not per-contact constants. Suitability $\psi$ enters $R^{env}$ twice, through beta_jt_env and through the reservoir lifetime $1/\delta_{jt}$, and one infection's lifetime is valued at today's $\delta_{jt}$. Under seasonal $\psi$, $R^{env} > 1$ is therefore not a growth threshold: in a high-$\psi$ season it assumes survival that will not last the infection's lifetime (up to ~200 days), and between seasons the reverse. R here is also not comparable to literature cholera R estimated with a ~5-day serial interval: for the same growth rate a longer generation interval gives a larger R. The renewal is per location: infectious people arriving through mobility (tau_i, pi_ij) drive the destination's human force of infection but are not in its $\Lambda^{hum}$, so in multi-location runs imported spread is credited to the destination's R_hum.

Central on this path is a calendar-date descriptor. The renewal on weighted-median incidence is phase-smoothed across members and reads closer to 1 than any coherent trajectory. add_reproductive_numbers( recompute_ci = TRUE) reports the MEDOID trajectory's R_t and the per-member peak statistic instead.

Posterior CI. Needs daily-consecutive per-member lines for both route channels starting on day 1; production artifacts thin lines on a stride, so the quantile columns are NA there (ci_source = "unavailable_strided_lines"). Use the re-simulation path for a CI. A cell's quantiles are reported only when members holding at least half the weight are defined there.

References

Cori A, Ferguson NM, Fraser C, Cauchemez S (2013). A new framework and software to estimate time-varying reproduction numbers during epidemics. American Journal of Epidemiology 178(9):1505-1512.