*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

`install.packages("finalsize")`

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")
::pak("epiverse-trace/finalsize") pak
```

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
\(R_0\), called \(R_{eff}\), from demographic and
susceptibility distribution data, while other helpers can convert
between \(R_0\) and the transmission
rate \(\lambda\).

Here, an example using social contact data from the
*socialmixr* package investigates the final size of an epidemic
when the disease has an R_{0} 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
library(finalsize)
# Load example POLYMOD data included with the package
data(polymod_uk)
# Define contact matrix (entry {ij} is contacts in group i reported by group j)
<- polymod_uk$contact_matrix
contact_matrix
# Define population in each age group
<- polymod_uk$demography_vector
demography_vector
# Define susceptibility of each group
<- matrix(
susceptibility data = c(1.0, 0.5, 0.5),
nrow = length(demography_vector),
ncol = 1
)
# Assume uniform susceptibility within age groups
<- matrix(
p_susceptibility data = 1.0,
nrow = length(demography_vector),
ncol = 1
)
# R0 of the disease
<- 1.5 # assumed for pandemic influenza
r0
# calculate the effective R0 using `r_eff()`
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
final_size(
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
```

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.

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.

```
citation("finalsize")
#> To cite package 'finalsize' in publications use:
#>
#> Gupte P, Van Leeuwen E, Kucharski A (2023). _finalsize: Calculate the
#> Final Size of an Epidemic_.
#> https://github.com/epiverse-trace/finalsize,
#> https://epiverse-trace.github.io/finalsize/.
#>
#> 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 = {https://github.com/epiverse-trace/finalsize,
#> https://epiverse-trace.github.io/finalsize/},
#> }
```

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. https://doi.org/10.1007/s11538-010-9623-3.

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. https://doi.org/10.1016/j.mbs.2016.10.012.

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. https://doi.org/10.1371/journal.ppat.1004206.

Miller, Joel C. 2012. “A Note on the Derivation of Epidemic Final
Sizes.” *Bulletin of Mathematical Biology* 74 (9): 2125–41. https://doi.org/10.1007/s11538-012-9749-6.