generation.time {R0}

Generation Time distribution

Description

Create an object of class GT representing a discretized Generation Time distribution, that can be subsequently passed to estimation routines.

Usage

generation.time(
  type = c("empirical", "gamma", "weibull", "lognormal"),
  val = NULL,
  truncate = NULL,
  step = 1,
  first.half = TRUE,
  p0 = TRUE
)

Arguments

type

Type of distribution (can be any of "empirical", "gamma", "weibull", or "lognormal")

val

Vector of values used for the empirical distribution, or c(mean, sd) if parametric.

truncate

Maximum extent of the GT distribution.

step

Time step used in discretization.

first.half

Boolean. When set to TRUE (default), the first probability is computed on a half period.

p0

Boolen. When set to TRUE the probability on day 0 is forced to 0.

Details

How the GT is discretized may have some impact on the shape of the distribution. For example, the distribution may be discretized in intervals of 1 time step starting at time 0, i.e. [0,1), [1,2), and so on. Or it may be discretized as [0,0.5), [0.5, 1.5), ... (the default).

If the GT is discretized from a given continuous distribution, the expected duration of the Generation Time will be less than the nominal, it will be in better agreement using the second discretization (default behavior).

If p0 is set to TRUE (default), the generation time distribution is set to 0 for day 0, meaning that the infectees generated by an infected individual will not become incident on the same day.

If no truncation is provided, the distribution will be truncated at 99.99% probability.

Value

A list with components:

GT

The probabilities for each time unit, starting at time 0.

time

The time at which probabilities are calculated.

mean

The mean of the discretized GT.

sd

The standard deviation of the discretized GT.

Author(s)

Pierre-Yves Boelle, Thomas Obadia

Examples

#Loading package
library(R0)

# GT for children at house(from Cauchemez PNAS 2011)

GT.chld.hsld1 <- generation.time("empirical", c(0,0.25,0.2,0.15,0.1,0.09,0.05,0.01))
plot(GT.chld.hsld1, col="green")
GT.chld.hsld1
# Discretized Generation Time distribution
# mean: 2.729412 , sd: 1.611636 
# [1] 0.00000000 0.29411765 0.23529412 0.17647059 0.11764706 0.10588235 0.05882353
# [8] 0.01176471

GT.chld.hsld2 <- generation.time("gamma", c(2.45, 1.38))
GT.chld.hsld2
# Discretized Generation Time distribution
# mean: 2.504038 , sd: 1.372760
# [1] 0.0000000000 0.2553188589 0.3247178420 0.2199060781 0.1144367560
# [6] 0.0515687896 0.0212246257 0.0082077973 0.0030329325 0.0010825594
#[11] 0.0003760069 0.0001277537


# GT for school & community
GTs1 <- generation.time("empirical", c(0,0.95,0.05))
plot(GTs1, col='blue')


plot(GT.chld.hsld1, ylim=c(0,0.5), col="red")
par(new=TRUE)
plot(GT.chld.hsld2, xlim=c(0,7), ylim=c(0,0.5), col="black")