superspreading (version 0.4.0)

probability_emergence: Calculate the probability a disease will emerge and cause a sustained outbreak (\(R > 1\)) based on R and initial cases

Description

The method for the evolution of pathogen emergence described in Antia et al. (2003) (tools:::Rd_expr_doi("10.1038/nature02104")). The model is a multi-type branching process model with an initial (wild-type) reproduction number, usually below 1, and a evolved reproduction number that is greater than 1, and thus can cause a sustained human-to-human epidemic. The reproduction number for a pathogen changes at the mutation_rate.

Usage

probability_emergence(
  R_wild,
  R_mutant,
  mutation_rate,
  num_init_infect,
  tol = 1e-10,
  max_iter = 1000
)

Value

A value with the probability of a disease emerging and causing an outbreak.

Arguments

R_wild

A number specifying the R parameter (i.e. average secondary cases per infectious individual) for the wild-type pathogen.

R_mutant

A number or vector of numbers specifying the R parameter (i.e. average secondary cases per infectious individual) for the mutant pathogen(s). If there is more than one value supplied to R_mutant, then the first element is the reproduction number for \(m - 1\) mutant and the last element is the reproduction number for the \(m\) mutant (i.e. fully evolved).

mutation_rate

A number specifying the mutation rate (\(\mu\)), must be between zero and one.

num_init_infect

An integer (or at least "integerish" if stored as double) specifying the number of initial infections.

tol

A number for the tolerance of the numerical convergence. Default is 1e-10.

max_iter

A number for the maximum number of iterations for the optimisation. Default is 1000.

Details

Following Antia et al. (2003), we assume that the mutation rate for all variants is the same.

References

Antia, R., Regoes, R., Koella, J. & Bergstrom, C. T. (2003) The role of evolution in the emergence of infectious diseases. Nature 426, 658–661. tools:::Rd_expr_doi("10.1038/nature02104")

See Also

probability_epidemic(), probability_extinct()

Examples

probability_emergence(
  R_wild = 0.5,
  R_mutant = 1.5,
  mutation_rate = 0.5,
  num_init_infect = 1
)