Effective reproduction number from susceptible depletion

This is the susceptible-depletion Rt, not the renewal-equation Rt. The two are routinely confused: R0 S / N is not the estimator Cori et al. (2013) define. Cori's Rt comes from the incidence curve and a serial-interval distribution and lives elsewhere in this package (Rtrenew). For the same reason this is not a duplicate of epirf.

Usage

Reffec(R0, S, N)

Arguments

R0

Basic reproduction number, non-negative.

S

Current susceptible count in [0, N].

N

Population size, positive.

Value

List with estimate, Rt, growing, susceptible_fraction, herd_immunity_threshold.

Details

The herd-immunity threshold falls out: Rt crosses one when the susceptible fraction reaches 1 / R0.

Formula: Rt = R0 S / N; growing iff Rt > 1.

References

Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28(4):365-382. doi:10.1007/BF00178324 .

Examples

Reffec(R0 = 5L, S = 5L, N = 5L)
#> $estimate
#> [1] 5
#> 
#> $Rt
#> [1] 5
#> 
#> $growing
#> [1] 1
#> 
#> $susceptible_fraction
#> [1] 1
#> 
#> $herd_immunity_threshold
#> [1] 0.8
#> 
#> $method
#> [1] "Effective reproduction number Rt = R0 S / N"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"