Lower edges, in years, of the default age groups: fine in childhood, where immunity and maternal immunity change fast, and coarse in adulthood.
Arguments
- max_age
lower edge, in years, of the oldest age group, which is open-ended. A single finite number of at least 20: below that the grid has too few anchors left to resolve the ages over which immunity develops.
- n_group
total number of age groups, the open-ended top group included. A whole number of at most 1e6, and at least one more than the number of anchor intervals below
max_age(14 formax_age = 80). Changing it refines or coarsens the whole grid while keeping its shape, as a grid-convergence check needs; run time is roughly proportional to it.
Details
Group edges are pinned at the conventional reporting ages, 0, 1, 2, 3, 5, 7,
10, 15, 20, 30, 40 and 60 years, so that the usual output bands fall on group
boundaries, and at 21, so that whole groups make up the year, [20, 21), from
which the IBM draws maternal immunity. Groups between two anchors are of
equal width. The groups are shared among the anchor intervals in proportion
to each interval's width in log(1 + age), weighted 1.25 below 5 years and
0.5 from 21 years; each interval gets at least one group, and the remainder
is allocated by largest remainder.
The width is logarithmic because what the grid has to resolve is the rise of
immunity with age, which is far closer to a function of log age than of age.
(log(1 + age) rather than log(age), which is infinite over the first
year; the offset is in years, so the allocation is not scale-free.) The
grading matters more than the count: at 53 groups an equal-width grid is four
times as far from the converged solution as a log-graded one (rms over the
age profile), and a grid of fixed monthly, quarterly, yearly and 5-yearly
sections, which over-resolves infancy and under-resolves everything above 15,
1.7 times as far. The grid's error is largest in clinical and severe
incidence among young children at high transmission; each age band's error
comes from the groups inside it, and the groups above 21 years have no
measurable effect on any child's incidence. The weights move groups to where
the error arises, and match the unweighted grid's accuracy with about a
quarter fewer groups.
The default, 118 groups, is the smallest grid on which every falciparum
claim in fleetcheck passes, not the most accurate; the deciding claim is
the clinical age profile's 3-5 year band at EIR 120, which needs 14 groups
between 3 and 5 years. fleet's age profile converges at first order: its
departure from the converged profile is fleet-low and halves with each
doubling of n_group. On the default grid the largest departure of the
EIR 20 clinical age profile is 3.2%, in the oldest band, which the weights
coarsen, and the rms 1.6%; on 53 groups they are 6.1% and 3.2%. Against the
IBM median, severe incidence at EIR 120 is 2% low on the default grid and 7%
low on 53 groups.
n_group = 53 runs over twice as fast and is adequate where a result does
not rest on the level of severe incidence, or of young children's incidence
at high transmission; n_group = 236 halves the grid's error for twice the
cost. Refinement does not remove the mean-field approximation itself, one
immunity value per stratum where the IBM holds a spread of infection
histories at the same age, so a persistent difference from the IBM is not
evidence that the grid is too coarse. fleetcheck measures both, in
validations/age-grid/run.R and the age-profile-clinical and
severe-allage-eir claims.
Output bands and intervention age targets that do not fall on a group edge are apportioned by the fraction of each group's width they cover; neither is snapped to the grid.
See also
ode_tuning(), which takes the grid as age_lower.
Examples
default_age_lower()
#> [1] 0.00000000 0.04545455 0.09090909 0.13636364 0.18181818 0.22727273
#> [7] 0.27272727 0.31818182 0.36363636 0.40909091 0.45454545 0.50000000
#> [13] 0.54545455 0.59090909 0.63636364 0.68181818 0.72727273 0.77272727
#> [19] 0.81818182 0.86363636 0.90909091 0.95454545 1.00000000 1.07142857
#> [25] 1.14285714 1.21428571 1.28571429 1.35714286 1.42857143 1.50000000
#> [31] 1.57142857 1.64285714 1.71428571 1.78571429 1.85714286 1.92857143
#> [37] 2.00000000 2.10000000 2.20000000 2.30000000 2.40000000 2.50000000
#> [43] 2.60000000 2.70000000 2.80000000 2.90000000 3.00000000 3.14285714
#> [49] 3.28571429 3.42857143 3.57142857 3.71428571 3.85714286 4.00000000
#> [55] 4.14285714 4.28571429 4.42857143 4.57142857 4.71428571 4.85714286
#> [61] 5.00000000 5.25000000 5.50000000 5.75000000 6.00000000 6.25000000
#> [67] 6.50000000 6.75000000 7.00000000 7.33333333 7.66666667 8.00000000
#> [73] 8.33333333 8.66666667 9.00000000 9.33333333 9.66666667 10.00000000
#> [79] 10.50000000 11.00000000 11.50000000 12.00000000 12.50000000 13.00000000
#> [85] 13.50000000 14.00000000 14.50000000 15.00000000 15.62500000 16.25000000
#> [91] 16.87500000 17.50000000 18.12500000 18.75000000 19.37500000 20.00000000
#> [97] 20.50000000 21.00000000 22.80000000 24.60000000 26.40000000 28.20000000
#> [103] 30.00000000 32.50000000 35.00000000 37.50000000 40.00000000 43.33333333
#> [109] 46.66666667 50.00000000 53.33333333 56.66666667 60.00000000 64.00000000
#> [115] 68.00000000 72.00000000 76.00000000 80.00000000
# open-ended top group from 60 years
default_age_lower(max_age = 60)
#> [1] 0.00000000 0.04166667 0.08333333 0.12500000 0.16666667 0.20833333
#> [7] 0.25000000 0.29166667 0.33333333 0.37500000 0.41666667 0.45833333
#> [13] 0.50000000 0.54166667 0.58333333 0.62500000 0.66666667 0.70833333
#> [19] 0.75000000 0.79166667 0.83333333 0.87500000 0.91666667 0.95833333
#> [25] 1.00000000 1.07142857 1.14285714 1.21428571 1.28571429 1.35714286
#> [31] 1.42857143 1.50000000 1.57142857 1.64285714 1.71428571 1.78571429
#> [37] 1.85714286 1.92857143 2.00000000 2.10000000 2.20000000 2.30000000
#> [43] 2.40000000 2.50000000 2.60000000 2.70000000 2.80000000 2.90000000
#> [49] 3.00000000 3.14285714 3.28571429 3.42857143 3.57142857 3.71428571
#> [55] 3.85714286 4.00000000 4.14285714 4.28571429 4.42857143 4.57142857
#> [61] 4.71428571 4.85714286 5.00000000 5.22222222 5.44444444 5.66666667
#> [67] 5.88888889 6.11111111 6.33333333 6.55555556 6.77777778 7.00000000
#> [73] 7.33333333 7.66666667 8.00000000 8.33333333 8.66666667 9.00000000
#> [79] 9.33333333 9.66666667 10.00000000 10.45454545 10.90909091 11.36363636
#> [85] 11.81818182 12.27272727 12.72727273 13.18181818 13.63636364 14.09090909
#> [91] 14.54545455 15.00000000 15.62500000 16.25000000 16.87500000 17.50000000
#> [97] 18.12500000 18.75000000 19.37500000 20.00000000 20.50000000 21.00000000
#> [103] 22.80000000 24.60000000 26.40000000 28.20000000 30.00000000 32.00000000
#> [109] 34.00000000 36.00000000 38.00000000 40.00000000 43.33333333 46.66666667
#> [115] 50.00000000 53.33333333 56.66666667 60.00000000
# under half the resolution everywhere, same shape, over twice as fast
length(default_age_lower(n_group = 53))
#> [1] 53