proportion_transmission {superspreading} | R Documentation |
Estimate what proportion of cases cause a certain proportion of transmission
Description
Calculates the proportion of cases that cause a certain percentage of transmission.
It is commonly estimated what proportion of cases cause 80% of transmission
(i.e. secondary cases).
This can be calculated using proportion_transmission()
at varying values of
R
and for different values of percentage transmission.
There are two methods for calculating the proportion of transmission,
p_{80}
(default) and t_{20}
, see method
argument or details for
more information.
Usage
proportion_transmission(
R,
k,
prop_transmission,
method = c("p_80", "t_20"),
simulate = FALSE,
...,
offspring_dist,
format_prop = TRUE
)
Arguments
R |
A |
k |
A |
prop_transmission |
A |
method |
A |
simulate |
A |
... |
dots not used, extra arguments supplied will cause a warning. |
offspring_dist |
An |
format_prop |
A |
Details
Calculates the expected proportion of transmission from a given
proportion of infectious cases. There are two methods to calculate this with
distinct formulations, p_{80}
and t_{20}
these can be specified
by the method
argument.
method = p_80
calculates relative transmission heterogeneity
from the offspring distribution of secondary cases, Z
, where the upper
proportion of the distribution comprise x\%
of total number of cases
given R0 and k, where x
is typically defined as 0.8 or 80%. e.g. 80%
of all transmissions are generated by the upper 20% of cases, or
p_80 = 0.2
, per the 80/20 rule. In this formulation, changes in R can
have a significant effect on the estimate of p_{80}
even when k
is constant. Importantly, this formulation does not allow for true
homogeneity when k = Inf
i.e. p_{80} = 0.8
.
method = t_20
calculates a similar ratio, instead in terms of
the theoretical individual reproductive number and infectiousness given
R_0
and k
. The individual reproductive number, \nu
, is
described in Lloyd-Smith et al. (2005), "as a random variable representing
the expected number of secondary cases caused by a particular infected
individual. Values for \nu
are drawn from a continuous gamma
probability distribution with population mean R_0
and dispersion
parameter k
, which encodes all variation in infectious histories of
individuals, including properties of the host and pathogen and environmental
circumstances." The value of k
corresponds to the shape parameters of
the gamma distribution which encodes the variation in the gamma-Poisson
mixture a.k.a. the negative binomial.
For method = t_20
, we define the upper proportion of infectiousness,
which is typically 0.2 i.e. the upper 20% most infectious
cases, again per the 80/20 rule. e.g. the most infectious 20% of cases,
are expected to produce 80% of all infections, or t_20 = 0.8
. Unlike
method = p_80
, changes in R have no effect on the estimate
of t_80 when k is constant, but R is still required for the underlying
calculation. This formulation does allow for true homogeneity when
k = Inf
i.e. t_20 = 0.2
, or t_80 = 0.8
.
Multiple values of R
and k
can be supplied and a <data.frame>
of
every combination of these will be returned.
The numerical calculation for method = p_80
uses random number generation
to simulate secondary contacts so the answers may minimally vary between
calls. The number of simulation replicates is fixed to 105.
Value
A <data.frame>
with the value for the proportion of cases for a
given value of R and k.
References
The analytical calculation is from:
Endo, A., Abbott, S., Kucharski, A. J., & Funk, S. (2020) Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China. Wellcome Open Research, 5. doi:10.12688/wellcomeopenres.15842.3
The t_{20}
method follows the formula defined in section 2.2.5 of the
supplementary material for:
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. Nov;438(7066):355–9. doi:10.1038/nature04153
The original code for the t_{20}
method is from ongoing work
originating from https://github.com/dcadam/kt and:
Adam, D., Gostic, K., Tsang, T., Wu, P., Lim, W. W., Yeung, A., Wong, J., Lau, E., Du, Z., Chen, D., Ho, L.-M., Martín-Sánchez, M., Cauchemez, S., Cobey, S., Leung, G., & Cowling, B. (2022) Time-varying transmission heterogeneity of SARS and COVID-19 in Hong Kong. doi:10.21203/rs.3.rs-1407962/v1
Examples
# example of single values of R and k
prop_transmission <- 0.8 # 80% of transmission
R <- 2
k <- 0.5
proportion_transmission(
R = R,
k = k,
prop_transmission = prop_transmission
)
# example with multiple values of k
k <- c(0.1, 0.2, 0.3, 0.4, 0.5, 1)
proportion_transmission(
R = R,
k = k,
prop_transmission = prop_transmission
)
# example with vectors of R and k
R <- c(1, 2, 3)
proportion_transmission(
R = R,
k = k,
prop_transmission = prop_transmission
)