Add data simulation functions

[Bisaloo]

Reopening #83 after repository clean-up.

[ntorresd]

This PR closes #57 .

[codecov-commenter]

Codecov Report

Merging #126 (bf211b8) into main (fe428e5) will increase coverage by 0.70%. The diff coverage is 79.74%.

:exclamation: Current head bf211b8 differs from pull request most recent head f5b5be6. Consider uploading reports for the commit f5b5be6 to get more accurate results

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##             main     #126      +/-   ##
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+ Coverage   76.06%   76.77%   +0.70%     
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  Files          10       10              
  Lines        1496     1563      +67     
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+ Hits         1138     1200      +62     
- Misses        358      363       +5     

Files	Coverage Δ
R/seroprevalence_data.R	77.19% <100.00%> (+27.19%)	:arrow_up:
R/visualisation.R	0.00% <0.00%> (ø)

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[ntorresd]

Hi @ben18785,

Continuing the conversation we had in #83, I implemented tests for different values of constant FoI using a large value for the sample size per age group and checked that the seroprevalence obtained for each is in accordance with the analytical solution of the serocatalytic model. I did the same for a stepwise decreasing time-varying FoI. In general, for a model without sero-reversion we have: $$\frac{dP(t)}{dt} = \lambda(t) (1 - P(t))$$ yielding the solution[ref] $$P(t) = 1 - \exp\left(-\int_0^{t'} \lambda(t')dt' \right),$$ Changing from time to ages, the implementation for the stepwise decreasing FoI looks like:

seed <- 1234
sample_size_by_age <- 10^7
tsur <- 2050
birth_year_min <- 2000

no_transm <- 0.0000000001
foi_sim <- c(rep(0.2, 25), rep(0.1, 10), rep(no_transm, 15))

sim_data <- generate_sim_data(foi = foi_sim,
                              sample_size_by_age = sample_size_by_age,
                              tsur = tsur,
                              birth_year_min = birth_year_min,
                              survey_label = 'sw_dec_foi',
                              seed = seed)

prev_exact <- 1 - exp(-cumsum(rev(foi_sim)))

expect_equal(sim_data$prev_obs, prev_exact, tolerance = TRUE)

It should be easy to test for other time-varying FoI in the limiting case.