Serial Interval and Case Reproduction Number Estimation

Provides methods to estimate serial intervals and time-varying case reproduction numbers from infectious disease outbreak data. Serial intervals measure the time between symptom onset in linked transmission pairs, while case reproduction numbers quantify how many secondary cases each infected individual generates over time. These parameters are essential for understanding transmission dynamics, evaluating control measures, and informing public health responses. The package implements the maximum likelihood framework from Vink et al. (2014) for serial interval estimation and the retrospective method from Wallinga & Lipsitch (2007) for reproduction number estimation. Originally developed for scabies transmission analysis but applicable to other infectious diseases including influenza, COVID-19, and emerging pathogens. Designed for epidemiologists, public health researchers, and infectious disease modelers working with outbreak surveillance data.

The mitey package

The mitey package is a lightweight package designed originally as a companion to the analyses presented by Ainslie et al. 2025 on scabies transmission. However, the methods featured in mitey are more widely applicable than in the context of scabies. Thus, the motivation behind creating the mitey package was twofold: 1) provide reproducible code to reproduce and also provides flexible, documented code for methods to estimate epidemiological quantities of interest.

Currently, mitey includes methods to estimate a) the mean and standard deviation of the serial interval distribution using a maximum likelihood framework developed by Vink et al. 2014 and b) the time-varying reproduction number using the method developed by Walling and Lipsitch 2007.

Installation

Install mitey from CRAN:

install.packages("mitey")

Or, install the development version of mitey from GitHub:

devtools::install_github("kylieainslie/mitey")

Installation time

system.time({
  devtools::install_github("kylieainslie/mitey", force = TRUE)
})
#> Using GitHub PAT from the git credential store.
#> Downloading GitHub repo kylieainslie/mitey@HEAD
#> pillar (1.10.2 -> 1.11.0) [CRAN]
#> Installing 1 packages: pillar
#> Installing package into '/private/var/folders/jt/rd3vkwv92yq6x0kb9k4m91zm0000gn/T/RtmpYIdFpK/temp_libpath1664f36a04f07'
#> (as 'lib' is unspecified)
#> 
#> The downloaded binary packages are in
#>  /var/folders/jt/rd3vkwv92yq6x0kb9k4m91zm0000gn/T//RtmpqYvwWP/downloaded_packages
#> ── R CMD build ─────────────────────────────────────────────────────────────────
#> * checking for file ‘/private/var/folders/jt/rd3vkwv92yq6x0kb9k4m91zm0000gn/T/RtmpqYvwWP/remotes1739348d85bf0/kylieainslie-mitey-6458b10/DESCRIPTION’ ... OK
#> * preparing ‘mitey’:
#> * checking DESCRIPTION meta-information ... OK
#> * checking for LF line-endings in source and make files and shell scripts
#> * checking for empty or unneeded directories
#> * building ‘mitey_0.1.0.tar.gz’
#> Installing package into '/private/var/folders/jt/rd3vkwv92yq6x0kb9k4m91zm0000gn/T/RtmpYIdFpK/temp_libpath1664f36a04f07'
#> (as 'lib' is unspecified)
#>    user  system elapsed 
#>   3.221   0.527   5.628

Main Functions

Example Usage

library(mitey)

#-----------------
# Serial Interval Estimation
#-----------------
icc_intervals <- c(rep(6,4),rep(7,8),rep(8,14),rep(9,31),rep(10,29),rep(11,42),rep(12,25),rep(13,16),rep(14,16), rep(15,10),rep(16,4),rep(17,2),rep(18,2))

# Estimate serial interval
si_results <- si_estim(icc_intervals)
si_results
#> $mean
#> [1] 10.91892
#> 
#> $sd
#> [1] 2.036239
#> 
#> $wts
#> [1] 3.625090e-02 9.146057e-01 3.012069e-16 4.913656e-02 7.797502e-22
#> [6] 6.801913e-06 6.863119e-28

# Plot fitted serial interval distribution
plot_si_fit(
  dat = icc_intervals,
  mean = si_results$mean[1],
  sd = si_results$sd[1],
  weights = c(si_results$wts[1], 
              si_results$wts[2] + si_results$wts[3],
              si_results$wts[4] + si_results$wts[5], 
              si_results$wts[6] + si_results$wts[7]),
  dist = "normal"
)

#-----------------
# Time-varying Reproduction Number Estimation
#-----------------
# Generate a synthetic epidemic using the generate_synthetic_epidemic function
set.seed(123)
true_r <- c(rep(2.5, 50), seq(2.5, 0.8, length.out = 30), rep(0.8, 100))

# Generate synthetic epidemic data
synthetic_data <- generate_synthetic_epidemic(
  true_r = true_r,      # Time-varying reproduction number
  si_mean = 5.2,        # Mean serial interval (days)
  si_sd = 1.72,         # SD of serial interval
  si_dist = "gamma",    # Distribution type
  initial_cases = 10    # Initial number of cases
)

incidence <- synthetic_data$incidence
dates <- synthetic_data$date

# Estimate time-varying reproduction number 
results <- wallinga_lipsitch(
  incidence = incidence, 
  dates = dates,
  si_mean = 5.2,          # mean serial interval in days
  si_sd = 1.72,           # serial interval SD
  si_dist = "gamma",      # serial interval distribution
  smoothing = 7,          # 7-day smoothing window
  bootstrap = TRUE,       # calculate bootstrap confidence intervals
  n_bootstrap = 100,      # number of bootstrap samples
  conf_level = 0.95       # 95% confidence intervals
)

head(results)
#>         date incidence        R R_corrected  R_lower  R_upper R_corrected_lower
#> 1 2023-01-01        10 2.731039    2.731039 2.011146 4.120939          2.011146
#> 2 2023-01-02         0 2.694590    2.694590 2.008012 3.692239          2.008012
#> 3 2023-01-03         1 2.664286    2.664286 2.064334 3.486878          2.064334
#> 4 2023-01-04         3 2.638675    2.638675 2.151772 3.354107          2.151772
#> 5 2023-01-05         9 2.550425    2.550425 2.108557 3.108038          2.108557
#> 6 2023-01-06        11 2.550200    2.550200 2.165532 3.064228          2.165532
#>   R_corrected_upper
#> 1          4.120939
#> 2          3.692239
#> 3          3.486878
#> 4          3.354107
#> 5          3.108038
#> 6          3.064228

Expected Run Times

Expected run times for the examples provided above are shown in the table below.

Vignettes

• A quick start guide showing examples of how to estimate the serial interval and time-varying reproduction number can be found here.

• A script that reproduces the results from Ainslie et al. 2025 can be found here.

• Validation of the method used to estimate the mean and standard deviation of the serial interval proposed by Vink et al. 2014 can be found here.

• Validation of the method used to estimate the time-varying reproduction number proposed by Wallinga and Lipsitch 2007 can be found here.

Data

Several data files are stored in the repo so that the results presented in Ainslie et al. 2025 are reproducible. Data files are stored in inst/extdata/data/. Below is a brief description of the different files.

• si_data.rds
  • Description: Data on date of symptom onset for scabies outbreaks described by Kaburi et al., Akunzirwe et al., Tjon-Kon-Fat et al., and Ariza et al.. For all outbreaks except Kaburi et al. the raw data was not available, thus the date of symptom onset data had to be reconstructed using the epidemic curve provided in the manuscript. The original data from Kaburi et al. is also available in the data directory (Kaburi_et_al_data_scabies.xlsx).
• scabies_data_yearly.xlsx
  • Description: Annual scabies incidence per 1000 people in the Netherlands from 2011-2023.
  • Source: Nivel
• scabies_data_consultation_weekly.xslx
  • Description: Weekly numbers of persons consulting for scabies (per 100,000 people) from 2011 to 2023 in the Netherlands as diagnosed by general practitioners (GPs). Note: Individuals in institutions (e.g., care homes, prisons) usually have their own health care provider and are generally not taken into account in GP registrations.
  • Source: Nivel

License

This package is distributed under the European Union Public License (EUPL) v1.2. See LICENSE file for details.

Citation

If you use this package, please cite both the manuscript and the software:

Manuscript

Ainslie, K.E.C., M. Hooiveld, J. Wallinga. (2025). Estimation of the epidemiological characteristics of scabies. Available at SSRN. https://dx.doi.org/10.2139/ssrn.5184990

Software

citation("mitey")
#> To cite package 'mitey' in publications use:
#> 
#>   Ainslie K (2025). _mitey: Toolkit to Estimate Infectious Disease
#>   Dynamics Parameters_. R package version 0.1.0, commit
#>   6458b1024fdf3e45ef5c6b5c800f5088ccd62b89,
#>   <https://github.com/kylieainslie/mitey>.
#> 
#> A BibTeX entry for LaTeX users is
#> 
#>   @Manual{,
#>     title = {mitey: Toolkit to Estimate Infectious Disease Dynamics Parameters},
#>     author = {Kylie Ainslie},
#>     year = {2025},
#>     note = {R package version 0.1.0, commit 6458b1024fdf3e45ef5c6b5c800f5088ccd62b89},
#>     url = {https://github.com/kylieainslie/mitey},
#>   }

Other

For reference, here are the original methodological papers:

• Vink et al. (2014). Serial intervals of respiratory infectious diseases: A systematic review and analysis. American Journal of Epidemiology, 180(9), 865-875.
• Wallinga, J., & Lipsitch, M. (2007). How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences, 274(1609), 599-604. doi: 10.1098/rspb.2006.3754

System Requirements

• R Version: R >= 4.0.0 (developed and tested with R 4.5.0)
• Operating Systems: Tested on
  • macOS (latest via GitHub Actions)
  • Windows Server (latest via GitHub Actions)
  • Ubuntu Linux 22.04+ (with R release and R-devel)

Dependencies

Contributing

Contributions to mitey are welcome! Please feel free to submit a pull request or open an issue to discuss potential improvements or report bugs.