Extinction probability for negative binomial branching process

Extinction probability for negative binomial branching process

nbbp_ep(r, k, tol = .Machine$double.eps)

Arguments

r

effective reproduction number

k

concentration parameter, smaller values mean distributions with higher variance, in the k = Inf limit, becomes a Poisson branching process

tol

tolerance passed to numerical solver

Value

a list, with $prob the extinction prob and $error a measure of numerical error

Details

See Nishiura et al 2012 (10.1016/j.jtbi.2011.10.039) equation 4. Probability that a branching process goes extinct. Solved numerically unless R < 1.0 (in which case the extinction probability is 1).