| Title: | Calculate Outbreak Probabilities for a Branching Process Model |
| Version: | 0.1.0 |
| Description: | Quantify outbreak risk posed by individual importers of a transmissible pathogen. Input parameters of negative binomial offspring distributions for the number of transmissions from each infected individual and initial number of infected. Calculate probabilities of final outbreak size and generations of transmission, as described in Toth et al. (2015) <doi:10.3201/eid2108.150170> and Toth et al. (2016) <doi:10.1016/j.epidem.2016.04.002>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| URL: | https://github.com/EpiForeSITE/branchingprocess, https://epiforesite.github.io/branchingprocess/ |
| BugReports: | https://github.com/EpiForeSITE/branchingprocess/issues |
| RoxygenNote: | 7.3.2 |
| Imports: | stats |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| VignetteBuilder: | knitr |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2025-04-24 20:50:24 UTC; runner |
| Author: | Damon Toth  [aut,
cre],
Erin Clancey
[ctb],
Centers for Disease Control and Prevention's Center for Forecasting and
Outbreak Analytics [fnd] (Cooperative agreement CDC-RFA-FT-23-0069) |
| Maintainer: | Damon Toth <damon.toth@hsc.utah.edu> |
| Repository: | CRAN |
| Date/Publication: | 2025-04-25 12:50:05 UTC |
Probability that one initial case leads to an outbreak that eventually dies out (stochastic extinction)
Description
Probability that one initial case leads to an outbreak that eventually dies out (stochastic extinction)
Usage
pExtinct(R, k)
Arguments
R |
Reproduction number: mean of negative binomial offspring distribution |
k |
Dispersion parameter of negative binomial offspring distribution |
Value
The probability of outbreak extinction
Author(s)
Damon Toth
Examples
# Probability that a single case leads to an extinct outbreak when the offspring distribution
# is negative binomial with mean 2 and dispersion parameter 0.5:
pExtinct(R=2,k=0.5)
Final outbreak size probability
Description
Final outbreak size probability
Usage
pFinalSize(n, j, R, k)
Arguments
n |
Number of initial cases in generation 0 |
j |
Total outbreak size (>= n). |
R |
Mean of negative binomial offspring distribution |
k |
Dispersion of negative binomial offspring distribution |
Value
The final size probability
Examples
# With 5 initial individuals and negative binomial offspring distribution with mean R=0.2
# and dispersion k=0.1, gives the probability of outbreak extinction with a total number
# final outbreak size of exactly 5 to 20 individuals (including the initial 5):
pFinalSize(5, 5:20, R=0.2, k=0.1)
Joint probability of outbreak final size and number of transmission generations
Description
Joint probability of outbreak final size and number of transmission generations
Usage
pFinalSizeAndGen(g, n, j, R, k)
Arguments
g |
Number of generations. |
n |
Number of initial cases |
j |
Final size |
R |
Reproduction number |
k |
Dispersion parameter |
Value
The joint probability of the final outbreak size and number of transmission generations
Author(s)
Damon Toth
Examples
# Probability that 1 initial infection leads to an outbreak of final size 20 over exactly
# 3 generations of transmission:
pFinalSizeAndGen(g=3,n=1,j=20,R=0.8,k=0.1)
Joint probability of outbreak final size and number of transmission generations with offspring distribution parameters switched after generation one
Description
Joint probability of outbreak final size and number of transmission generations with offspring distribution parameters switched after generation one
Usage
pFinalSizeAndGenSwitch1(g, n, j, R0, k0, Rc, kc)
Arguments
g |
Number of generations |
n |
Number of initial cases |
j |
Final size |
R0 |
Mean of negative binomial offspring distribution from generation one |
k0 |
Dispersion of negative binomial offspring distribution from generation one |
Rc |
Mean of negative binomial offspring distribution from generation two on |
kc |
Dispersion of negative binomial offspring distribution from generation two on |
Value
The joint probability of outbreak final size and number of transmission generations
Author(s)
Damon Toth
Examples
# Probability that 1 initial infection leads to an outbreak of final size 20 over exactly
# 3 generations of transmission:
pFinalSizeAndGenSwitch1(g=3,n=1,j=20,R0=2,k0=0.1,Rc=0.5,kc=1)
Probability of final outbreak size with offspring distribution parameters switched after generation one
Description
pFinalSizeSwitch1 is the probability that n initial cases lead to an extinguished outbreak of total size j after any number of transmission generations (j includes the n initial cases)
Usage
pFinalSizeSwitch1(n, j, R0, k0, Rc, kc)
Arguments
n |
Number of initial cases in generation 0 |
j |
Total outbreak size (>= n). |
R0 |
Mean of negative binomial offspring distribution from generation one |
k0 |
Dispersion of negative binomial offspring distribution from generation one |
Rc |
Mean of negative binomial offspring distribution from generation two on |
kc |
Dispersion of negative binomial offspring distribution from generation two on |
Value
The probability of the final outbreak size
Examples
#With 5 initial cases, the probability that the final outbreak size is 5 to 20
#(including the initial 5):
pFinalSizeSwitch1(n=5, j=5:20, R0=2, k0=0.1, Rc=0.2, kc=0.1)
Probability that one initial case leads to an outbreak lasting less than g generations of transmission.
Description
Probability that one initial case leads to an outbreak lasting less than g generations of transmission.
Usage
pGen(gMax, R, k)
Arguments
gMax |
Maximum number of generations. |
R |
Reproduction number. |
k |
Dispersion parameter. |
Value
A vector of probabilities for each number of generations from 1 to gmax
Author(s)
Damon Toth
Examples
# Probability of outbreak lasting less than 1,2,3,...,10 generations:
pGen(gMax=10, R=0.9, k=0.1)
Probability that one initial case leads to an outbreak lasting less than g generations of transmission, with offspring distribution parameters switched after generation one.
Description
Probability that one initial case leads to an outbreak lasting less than g generations of transmission, with offspring distribution parameters switched after generation one.
Usage
pGenSwitch1(gMax, R0, k0, Rc, kc)
Arguments
gMax |
Maximum number of generations |
R0 |
Basic reproduction number: mean of negative binomial offspring distribution from generation one |
k0 |
Dispersion of negative binomial offspring distribution from generation one |
Rc |
Control reproduction number: mean of negative binomial offspring distribution from generation two plus |
kc |
Dispersion of negative binomial offspring distribution from generation two plus |
Value
A vector of probabilities for each number of generations from 1 to gmax
Author(s)
Damon Toth
Examples
# Probability of outbreak lasting less than 1,2,3,...,10 generations:
pGenSwitch1(gMax=10, R0=3, k0=0.1, Rc=0.5, kc=1)
Probability of y total transmission directly from x independent infected individuals
Description
Probability of y total transmission directly from x independent infected individuals
Usage
pNextGenSize(x, y, R, k)
Arguments
x |
Number of infected individuals in generation n |
y |
Number of total transmissions in generation n+1 |
R |
Mean of negative binomial offspring distribution |
k |
Dispersion of negative binomial offspring distribution |
Value
The probability of the given number of transmissions
Examples
# With 5 individuals in this generation, what is the probability of
# 0 to 15 transmissions in the next generation?
pNextGenSize(x=5, y=0:15, R=0.2, k=0.1)
Probability that n initial cases lead to an outbreak that lasts at least g generations of transmission AND has exactly j total cases after generation g
Description
Probability that n initial cases lead to an outbreak that lasts at least g generations of transmission AND has exactly j total cases after generation g
Usage
pSizeAtGen(g, n, j, R, k)
Arguments
g |
Number of generations of transmission |
n |
Number of initial cases |
j |
Total size of outbreak after generation g |
R |
Reproduction number: mean of negative binomial offspring distribution |
k |
Dispersion parameter of negative binomial offspring distribution |
Value
The probability of the given outbreak size at the given generation
Author(s)
Damon Toth
Examples
#Probability that 10 initial cases leads to an outbreak lasting at least
# 3 transmission generations and is of exact size 30 after 3 generations
pSizeAtGen(g=3,n=10,j=30,R=2,k=0.5)
Probability that n initial cases lead to an outbreak that lasts at least g generations of transmission AND has exactly j total cases after generation g, with offspring distribution parameters switched after generation one
Description
Probability that n initial cases lead to an outbreak that lasts at least g generations of transmission AND has exactly j total cases after generation g, with offspring distribution parameters switched after generation one
Usage
pSizeAtGenSwitch1(g, n, j, R0, k0, Rc, kc)
Arguments
g |
Number of generations of transmission |
n |
Number of initial cases |
j |
Total size of outbreak after generation g |
R0 |
Basic reproduction number: mean of negative binomial offspring distribution from generation one |
k0 |
Dispersion parameter of negative binomial offspring distribution from generation one |
Rc |
Control reproduction number: mean of negative binomial offspring distribution from generation two plus |
kc |
Dispersion parameter of negative binomial offspring distribution from generation two plus |
Value
The probability of the given outbreak size at the given transmission generation
Author(s)
Damon Toth
Examples
#Probability that 10 initial cases leads to an outbreak lasting at least
# 3 transmission generations and is of exact size 30 after 3 generations
pSizeAtGenSwitch1(g=3,n=10,j=30,R0=2,k0=0.5,Rc=0.5,kc=1)