tailoffspringQ {modelSSE}

The "20/80" rule

Description

To calculate proportion of (Q) offspring cases generated from proportion of (P) the most infectious index cases with pre-defined epidemiological parameters for the offspring distribution.

Usage

tailoffspringQ(
  P = 0.2,
  epi.para = list(mean = 1, disp = 0.5, shift = 0.2),
  offspring.type = "D",
  n.seed = 1000
)

mostinfectiousP(
  Q = 0.8,
  epi.para = list(mean = 1, disp = 0.5, shift = 0.2),
  offspring.type = "D",
  n.seed = 1000
)

Arguments

P, Q

A scalar, or a vector of probability (i.e., ranging from 0 to 1).

epi.para

A list (list) of pre-defined epidemiological parameters for offspring distribution, in the format of list(mean = ?, disp = ?, shift = ?), where the three parameters accept non-negative values. Each parameter must be a scalar. For Delaporte distribution, the value of mean should be larger than the value of shift.

offspring.type

A character label (character) indicating the type of distribution used to describe the offspring distribution. It only accepts one of the following values:

• "D" indicates the Delaporte distribution,

• "NB" indicates the negative binomial distribution,

• "G" indicates the geometric distribution, or

• "P" indicates the Poisson distribution.

By default, offspring.type = 'D'.

n.seed

A positive integer, for the number of seeds used to solve P or Q numerically. By default, n.seed = 1000, and no need to change the default setting here unless for special reasons.

Value

Function tailoffspringQ() returns the proportion of (Q) offspring cases generated from proportion of (P) index cases, where (P) is given.

Function mostinfectiousP() returns the proportion of (P) index cases that generated proportion of (Q) offspring cases, where (Q) is given.

Note

When n.seed is large, e.g., n.seed > 100000, the functions could take minutes to complete. As such, we do not recommend the users to change the default setting of n.seed unless for special reasons.

Each parameter in epi.para = list(mean = ?, disp = ?, shift = ?) should be a scalar, which means vector is not allowed here.

References

Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading and the effect of individual variation on disease emergence. Nature. 2005;438(7066):355-359. doi:10.1038/nature04153

Endo A, Abbott S, Kucharski AJ, Funk S. Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China. Wellcome Open Research. 2020;5:67. doi:10.12688/wellcomeopenres.15842.3

Adam DC, Wu P, Wong JY, Lau EH, Tsang TK, Cauchemez S, Leung GM, Cowling BJ. Clustering and superspreading potential of SARS-CoV-2 infections in Hong Kong. Nature Medicine. 2020;26(11):1714-9. doi:10.1038/s41591-020-1092-0

Zhao S, Chong MK, Ryu S, Guo Z, He M, Chen B, Musa SS, Wang J, Wu Y, He D, Wang MH. Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility. PLoS Computational Biology. 2022;18(6):e1010281. doi:10.1371/journal.pcbi.1010281

See Also

d_offspringdistn

Examples

## reproducing the results in Endo, et al. (2020) https://doi.org/10.12688/wellcomeopenres.15842.3,
## where ~80% offspring cases were generated from ~10% index cases
## with parameters R of ~2.5 (ranging from 2 to 3) and
## k of ~0.1 (ranging from 0.05 to 0.20) under NB distribution.
tailoffspringQ(
  P = 0.10,
  epi.para = list(mean = 2.5, disp = 0.10, shift = 0.2),
  offspring.type = "NB"
)
mostinfectiousP(
  Q = 0.80,
  epi.para = list(mean = 2.5, disp = 0.10, shift = 0.2),
  offspring.type = "NB"
)


## reproducing the results in Adam, et al. (2020) https://doi.org/10.1038/s41591-020-1092-0,
## where ~80% offspring cases were generated from ~19% index cases
## with parameters R of 0.58 and k of 0.43 under NB distribution.
tailoffspringQ(
  P = 0.19,
  epi.para = list(mean = 0.58, disp = 0.43, shift = 0.2),
  offspring.type = "NB"
)
mostinfectiousP(
  Q = 0.80,
  epi.para = list(mean = 0.58, disp = 0.43, shift = 0.2),
  offspring.type = "NB"
)