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finalsize is an R package to calculate the final size of a SIR epidemic in populations with heterogeneity in social contacts and infection susceptibility.

finalsize provides estimates for the total proportion of a population infected over the course of an epidemic, and can account for a demographic distribution (such as age groups) and demography-specific contact patterns, as well as for heterogeneous susceptibility to infection between groups (such as due to age-group specific immune responses) and within groups (such as due to immunisation programs).

finalsize implements methods outlined in Andreasen (2011), Miller (2012), Kucharski et al. (2014), and Bidari et al. (2016).

finalsize can help provide rough estimates of the effectiveness of pharmaceutical interventions in the form of immunisation programmes, or the effect of naturally acquired immunity through previous infection (see the vignette).

finalsize relies on Eigen via RcppEigen for fast matrix algebra, and is developed at the Centre for the Mathematical Modelling of Infectious Diseases at the London School of Hygiene and Tropical Medicine as part of the Epiverse-TRACE.


The package can be installed from CRAN using


Development version

The current development version of finalsize can be installed from Github using the remotes package. The development version documentation can be found here.

if(!require("pak")) install.packages("pak")

Quick start

The main function in finalsize is final_size(), which calculates the final size of an epidemic. Helper functions included in finalsize are provided to calculate the effective R0, called Reff, from demographic and susceptibility distribution data, while other helpers can convert between R0 and the transmission rate λ.

Here, an example using social contact data from the socialmixr package investigates the final size of an epidemic when the disease has an R0 of 1.5, and given three age groups of interest — 0-19, 20-39 and 40+. The under-20 age group is assumed to be fully susceptible to the disease, whereas individuals aged over 20 are only half as susceptible as those under 20.

# load finalsize

# Load example POLYMOD data included with the package

# Define contact matrix (entry {ij} is contacts in group i reported by group j)
contact_matrix <- polymod_uk$contact_matrix

# Define population in each age group
demography_vector <- polymod_uk$demography_vector

# Define susceptibility of each group
susceptibility <- matrix(
  data = c(1.0, 0.5, 0.5),
  nrow = length(demography_vector),
  ncol = 1

# Assume uniform susceptibility within age groups
p_susceptibility <- matrix(
  data = 1.0,
  nrow = length(demography_vector),
  ncol = 1

# R0 of the disease
r0 <- 1.5 # assumed for pandemic influenza

# calculate the effective R0 using `r_eff()`
  r0 = r0,
  contact_matrix = contact_matrix,
  demography_vector = demography_vector,
  susceptibility = susceptibility,
  p_susceptibility = p_susceptibility
#> [1] 1.171758

# Calculate the proportion of individuals infected in each age group
  r0 = r0,
  contact_matrix = contact_matrix,
  demography_vector = demography_vector,
  susceptibility = susceptibility,
  p_susceptibility = p_susceptibility
#>   demo_grp   susc_grp susceptibility p_infected
#> 1   [0,20) susc_grp_1            1.0 0.32849966
#> 2  [20,40) susc_grp_1            0.5 0.10532481
#> 3      40+ susc_grp_1            0.5 0.06995193

Package vignettes

More details on how to use finalsize can be found in the online documentation as package vignettes, under “Articles”.


To report a bug please open an issue.


Contributions to finalsize are welcomed. Please follow the package contributing guide.

Code of conduct

Please note that the finalsize project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.

Citing this package

#> To cite package 'finalsize' in publications use:
#>   Gupte P, Van Leeuwen E, Kucharski A (2023). _finalsize: Calculate the
#>   Final Size of an Epidemic_.
#> A BibTeX entry for LaTeX users is
#>   @Manual{,
#>     title = {finalsize: Calculate the Final Size of an Epidemic},
#>     author = {Pratik Gupte and Edwin {Van Leeuwen} and Adam Kucharski},
#>     year = {2023},
#>     note = {,
#>   }


Andreasen, Viggo. 2011. “The Final Size of an Epidemic and Its Relation to the Basic Reproduction Number.” Bulletin of Mathematical Biology 73 (10): 2305–21.
Bidari, Subekshya, Xinying Chen, Daniel Peters, Dylanger Pittman, and Péter L. Simon. 2016. “Solvability of Implicit Final Size Equations for SIR Epidemic Models.” Mathematical Biosciences 282 (December): 181–90.
Kucharski, Adam J., Kin O. Kwok, Vivian W. I. Wei, Benjamin J. Cowling, Jonathan M. Read, Justin Lessler, Derek A. Cummings, and Steven Riley. 2014. “The contribution of social behaviour to the transmission of influenza A in a human population.” PLoS pathogens 10 (6): e1004206.
Miller, Joel C. 2012. “A Note on the Derivation of Epidemic Final Sizes.” Bulletin of Mathematical Biology 74 (9): 2125–41.