Calculate a growth rate from a reproduction number and an infectivity profile,

This solves the relationship between $R_t$ and growth rates as described by Wallinga and Lipsitch, to get a growth rate from $R_t$ and infectivity profile.

Usage

inv_wallinga_lipsitch(
  Rt,
  y = i_empirical_ip,
  a1 = seq(0.5, length.out = length(y)),
  a0 = dplyr::lag(a1, default = 0)
)

Arguments

Rt

a vector of reproduction numbers

y

an empirical infectivity profile as a probability vector or as a dataframe of format: A dataframe containing the following columns:

• boot (anything + default(1)) - a bootstrap identifier

• probability (proportion) - the probability of new event during this period.

• a0 (double) - the beginning of the time period (in days)

• a1 (double) - the end of the time period (in days)

Minimally grouped by: boot (and other groupings allowed).

a1

the end time of the infectivity profile probability estimate (defaults to 0.5,1.5,2.5,...).

a0

the start time of the infectivity profile probability estimate (defaults to 0,0.5,1.5,...).

Value

an vector of growth rates

Details

This function uses a single empirical distribution for the infectivity profile / generation time. If multiple are provided then the average central value is chosen (i.e. this does not propagate uncertainty in infectivity profile)

Examples

inv_wallinga_lipsitch(Rt=seq(0.5,2.5,length.out=9), y=example_ip())
#> [1] -0.13146405 -0.05656638  0.00000000  0.04589395  0.08478342  0.11865588
#> [7]  0.14875936  0.17591664  0.20070417