Final outbreak size for negative binomial branching process

Final outbreak size for negative binomial branching process

dnbbp(x, r, k, condition_on_extinction = FALSE)

pnbbp(q, r, k)

rnbbp(n, r, k, condition_on_extinction = FALSE, max_size = 1e+06)

Arguments

x

final outbreak size, including the index case

r

effective reproduction number

k

dispersion parameter: when <1, overdispersed

condition_on_extinction

logical, should we condition_on_extinction the process on extinction (TRUE) or not (FALSE)

q

as x

n

number of samples to draw

max_size

when drawing samples, the pmf for non-infinite chains is truncated to this size determined. Infinite chains are still possible (and return Inf).

Details

In this model, every individual infects a Negative-Binomially-distributed number of additional individuals. The distribution is on the final number of infected individuals, including the index case.

Blumberg et al 2014 (10.1093/aje/kwu068) equation 1, calls the terms in this PMF r(j), the probability that a transmission chain will have true size j.

When R >= 1.0, the process may not go extinct. In these cases, the outcome is dependent on the choice of condition_on_extinction.

When R >= 1 and condition_on_extinction == FALSE (the default), chains are allowed to become infinitely large. In this case, rnbbp will record this size as Inf.

When R >= 1 and condition_on_extinction == TRUE, the model is conditioned on all chains going extinct. No infinitely-large chains are allowed.

Nishiura et al 2012 (https://doi.org/10.1016/j.jtbi.2011.10.039) discuss the R > 1 case when conditioning on extinction.