Probability that an outbreak will be contained

Outbreak containment is defined as outbreak extinction when simulate = FALSE. When simulate = FALSE, probability_contain() is equivalent to calling probability_extinct().

When simulate = TRUE, outbreak containment is defined by the case_threshold (default = 100) and outbreak_time arguments. Firstly, case_threshold sets the size of the transmission chain below which the outbreak is considered contained. Secondly, outbreak_time sets the time duration from the start of the outbreak within which the outbreak is contained if there is no more onwards transmission beyond this time. When setting an outbreak_time, a generation_time is also required. case_threshold and outbreak_time can be jointly set. Overall, when simulate = TRUE, containment is defined as the size and time duration of a transmission chain not reaching the case_threshold and outbreak_time, respectively.

Usage

probability_contain(
  R,
  k,
  num_init_infect,
  ind_control = 0,
  pop_control = 0,
  simulate = FALSE,
  ...,
  case_threshold = 100,
  outbreak_time = Inf,
  generation_time = NULL,
  offspring_dist
)

Arguments

R: A number specifying the \(R\) parameter (i.e. average secondary cases per infectious individual).
k: A number specifying the \(k\) parameter (i.e. dispersion in offspring distribution from fitted negative binomial).
num_init_infect: An integer (or at least "integerish" if stored as double) specifying the number of initial infections.
ind_control: A numeric specifying the strength of individual-level control measures. These control measures assume that infected individuals do not produce any secondary infections with probability ind_control, thus increasing the proportion of cases that do not create any subsequent infections. The control measure is between 0 (default) and 1 (maximum).
pop_control: A numeric specifying the strength of population-level control measures that reduce the transmissibility of all cases by a constant factor. Between 0 (default) and 1 (maximum).
simulate: A logical boolean determining whether the probability of containment is calculated analytically or numerically using a stochastic branching process model. Default is FALSE which calls probability_extinct(), setting to TRUE uses a branching process and enables setting the case_threshold, outbreak_time and generation_time arguments.
...: <dynamic-dots> Named elements to replace default arguments in .chain_sim(). See details.
case_threshold: A number for the threshold of the number of cases below which the epidemic is considered contained. case_threshold is only used when simulate = TRUE.
outbreak_time: A number for the time since the start of the outbreak to determine if outbreaks are contained within a given period of time. outbreak_time is only used when simulate = TRUE.
generation_time: A function to generate generation times. The function must have a single argument and return a numeric vector with generation times. See details for example. The function can be defined or anonymous. generation_time is only used when simulate = TRUE.
offspring_dist: An <epiparameter> object. An S3 class for working with epidemiological parameters/distributions, see epiparameter::epiparameter().

Value

A number for the probability of containment.

Details

When using simulate = TRUE, the default arguments to simulate the transmission chains with .chain_sim() are 10⁵ replicates, a negative binomial (nbinom) offspring distribution, parameterised with R (and pop_control if > 0) and k.

When setting the outbreak_time argument, the generation_time argument is also required. The generation_time argument requires a random number generator function. For example, if we assume the generation time is lognormally distributed with meanlog = 1 and sdlog = 1.5, then we can define the function to pass to generation_time as:

function(x) rlnorm(x, meanlog = 1, sdlog = 1.5)

References

Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E., & Getz, W. M. (2005) Superspreading and the effect of individual variation on disease emergence. Nature, 438(7066), 355-359. doi:10.1038/nature04153

Examples