p_infected > susceptibility for high R0 values

Hello! I have been testing the package to model diseases like measles or pertussis with high R0 values and I wanted to know if there are any limitations regarding the range of R0s the calculations of final size are acceptable/doable for. For example, I was replicating the example in: https://epiverse-trace.github.io/finalsize/articles/varying_susceptibility.html using an r0 of 10 and the p_infected that the model returns is bigger than the suscetpibility provided for the different age groups. Code follows:

library(tidyverse)
library(finalsize)

# get UK polymod data
polymod <- socialmixr::polymod
contact_data <- socialmixr::contact_matrix(
polymod,
countries = "United Kingdom",
age.limits = c(0, 5, 18, 40, 65),
symmetric = TRUE
)

# get the contact matrix and demography data
contact_matrix <- t(contact_data$matrix)
demography_vector <- contact_data$demography$population

# scale the contact matrix so the largest eigenvalue is 1.0
contact_matrix <- contact_matrix / max(Re(eigen(contact_matrix)$values))

# divide each row of the contact matrix by the corresponding demography
contact_matrix <- contact_matrix / demography_vector

n_demo_grps <- length(demography_vector)

r0 <- 10

susc_variable <- matrix(
data = c(0.75, 0.8, 0.85, 0.9, 1.0)
)
n_susc_groups <- 1L

p_susc_uniform <- matrix(
data = 1.0,
nrow = n_demo_grps,
ncol = n_susc_groups
)

final_size_heterog <- final_size(
r0 = r0,
contact_matrix = contact_matrix,
demography_vector = demography_vector,
susceptibility = susc_variable,
p_susceptibility = p_susc_uniform,
solver = 'iterative'
)

final_size_heterog

The results are:

I noticed that when just calling final_size(15), there are some warnings (though not in the previous case)

Thank you for the attention, as well as the package!

Start by running the supplied final_size() example with r0 = 10 and then the simpler final_size(15) call, noting the returned warnings and p_infected values. Trace the iterative solver behavior for heterogeneous susceptibility and compare its results with the supplied susceptibility values. Done means determining whether this is expected behavior or a calculation limitation, then documenting or correcting the confirmed issue.

Written by the indexing model from the issue text.