Discretized Generation Time Distribution Assuming A Shifted Gamma Distribution
discr_si computes the discrete distribution of the serial interval,
assuming that the serial interval is shifted Gamma distributed, with shift 1.
discr_si(k, mu, sigma)
k |
Positive integer, or vector of positive integers for which the discrete distribution is desired. |
mu |
A positive real giving the mean of the Gamma distribution. |
sigma |
A non-negative real giving the standard deviation of the Gamma distribution. |
Assuming that the serial interval is shifted Gamma distributed with mean μ, standard deviation σ and shift 1, the discrete probability w_k that the serial interval is equal to k is:
w_k = kF_{\{μ-1,σ\}}(k)+(k-2)F_{\{μ-1,σ\}} (k-2)-2(k-1)F_{\{μ-1,σ\}}(k-1)\\ +(μ-1)(2F_{\{μ-1+\frac{σ^2}{μ-1}, σ√{1+\frac{σ^2}{μ-1}}\}}(k-1)- F_{\{μ-1+\frac{σ^2}{μ-1}, σ√{1+\frac{σ^2}{μ-1}}\}}(k-2)- F_{\{μ-1+\frac{σ^2}{μ-1}, σ√{1+\frac{σ^2}{μ-1}}\}}(k))
where F_{\{μ,σ\}} is the cumulative density function of a Gamma distribution with mean μ and standard deviation σ.
Gives the discrete probability w_k that the serial interval is equal to k.
Anne Cori a.cori@imperial.ac.uk
Cori, A. et al. A new framework and software to estimate time-varying reproduction numbers during epidemics (AJE 2013).
## Computing the discrete serial interval of influenza
mean_flu_si <- 2.6
sd_flu_si <- 1.5
dicrete_si_distr <- discr_si(seq(0, 20), mean_flu_si, sd_flu_si)
plot(seq(0, 20), dicrete_si_distr, type = "h",
lwd = 10, lend = 1, xlab = "time (days)", ylab = "frequency")
title(main = "Discrete distribution of the serial interval of influenza")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.