Computes the time-varying reproduction number (Rt), defined as the average number of secondary infections generated by each infected individual at time t, accounting for the generation interval distribution: $$R_t = \frac{I_t}{\sum_{k=0}^{\tau_{\max}-1} I_{t-k} \cdot \frac{g(k)}{g_a}}$$
Usage
Rt(fitted_model, gi_dist, tau_max = 7, ...)
# S3 method for class 'ps'
Rt(fitted_model, gi_dist, tau_max = 7, ...)
# S3 method for class 'rw'
Rt(fitted_model, gi_dist, tau_max = 7, ...)
# S3 method for class 'ps_single'
Rt(fitted_model, gi_dist, tau_max = 7, ...)
# S3 method for class 'rw_single'
Rt(fitted_model, gi_dist, tau_max = 7, ...)Arguments
- fitted_model
Fitted model object with class
EpiStrainDynamics.fit- gi_dist
Function returning the generation interval probability for a given day. Must accept a numeric vector and return a non-negative numeric vector of the same length; does not need to sum to 1 (see Description).
- tau_max
Integer maximum generation interval in days (default: 7)
- ...
Additional arguments passed to metrics calculation
Value
named list of class EpiStrainDynamics.metric containing a dataframe
of the calculated metric outcome ($measure), the fit object ($fit), and the
constructed model object ($constructed_model). The measure data frame
contains the median of the epidemiological quantity (y), the 50% credible
interval of the quantity (lb_50 & ub_50), the 95% credible interval
(lb_95 & ub_95), the proportion greater than a defined threshold value
(prop), the pathogen name (pathogen), and the time label (time).
Details
Where:
\(I_t = \exp(\log\text{-incidence}_t)\) is the current incidence
\(g(k)\) is the generation interval probability for day k
\(g_a = \sum_{k=0}^{\tau_{\max}-1} g(k)\) is the normalization constant
\(\tau_{\max}\) is the maximum generation interval in days
This metric quantifies current transmission potential by comparing present incidence to the weighted historical incidence that could have generated it, where:
\(R_t > 1\): Epidemic is growing (each case generates >1 secondary case)
\(R_t = 1\): Epidemic is stable (replacement level transmission)
\(R_t < 1\): Epidemic is declining (each case generates <1 secondary case)
Threshold of 1 is epidemiologically meaningful for control decisions
Generation interval considerations:
Accounts for transmission timing using probability distribution \(g(k)\)
Recent cases contribute more to current transmission potential
Accepts user-defined generation interval distributions, validated for structural properties (vectorized, non-negative, finite)
Does not need to sum to 1 – normalized internally using \(g_a = \sum_{k=0}^{\tau_{\max}-1} g(k)\)
Validation does not assess whether the shape is epidemiologically plausible (e.g. unimodal, decaying); as with other Rt estimation methods, supplying a distribution informed by published estimates for the pathogen(s) being modelled is the user's responsibility
This metric function can be run directly on the fitted model output.
See also
Other metrics:
growth_rate(),
incidence(),
proportion()
Examples
if (FALSE) { # interactive()
mod <- construct_model(
pathogen_structure = single(
case_timeseries = sarscov2$cases,
time = sarscov2$date
),
method = random_walk()
)
fit <- fit_model(mod)
rt <- Rt(fit, gi_dist = function(x) 4 * x * exp(-2 * x), tau_max = 7)
}