Renewal-equation forecast

Formula: I_t = R_t sum_{s>=1} I_{t-s} w_s, where w is the generation interval distribution (normalised to sum to one) and Lambda_t = sum_s I_{t-s} w_s is the total infectiousness at time t. Forward projection feeds each simulated incidence back into Lambda for the following step. Read backwards the same identity gives the instantaneous reproduction number, Rhat_t = I_t / Lambda_t.

Usage

Ferror(incidence, Rt, gen_int)

Arguments

incidence

Observed incidence I_1..I_n.

Rt

Reproduction number per forecast step; a scalar is held constant over a one-step horizon.

gen_int

Generation-interval weights w_1..w_S at lags 1..S; non-negative, renormalised internally.

Value

List with estimate, forecast, lambda_, total, Rt_implied, horizon, n, method.

References

Fraser (2007), PLoS ONE 2(8):e758, doi:10.1371/journal.pone.0000758.

Examples

Ferror(incidence = c(1, 2, 3, 4, 5, 6, 7, 8), Rt = c(1, 2, 3, 4, 5, 6, 7, 8),
  gen_int = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 356.8365
#> 
#> $forecast
#> [1]   3.333333   8.351852  14.918210  23.513546  35.519285  53.729180  83.366206
#> [8] 134.104911
#> 
#> $lambda_
#> [1]  3.333333  4.175926  4.972737  5.878386  7.103857  8.954863 11.909458
#> [8] 16.763114
#> 
#> $total
#> [1] 356.8365
#> 
#> $Rt_implied
#> numeric(0)
#> 
#> $horizon
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Renewal-equation forecast"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"