# Estimate Infections, the Time-Varying Reproduction Number and the Rate of Growth

Source:`R/estimate_infections.R`

`estimate_infections.Rd`

Uses a non-parametric approach to reconstruct cases by date of infection
from reported cases. It uses either a generative Rt model or non-parametric
back calculation to estimate underlying latent infections and then maps
these infections to observed cases via uncertain reporting delays and a
flexible observation model. See the examples and function arguments for the
details of all options. The default settings may not be sufficient for your
use case so the number of warmup samples (`stan_args = list(warmup)`

) may
need to be increased as may the overall number of samples. Follow the links
provided by any warnings messages to diagnose issues with the MCMC fit. It
is recommended to explore several of the Rt estimation approaches supported
as not all of them may be suited to users own use cases. See
here
for an example of using `estimate_infections`

within the `epinow`

wrapper to
estimate Rt for Covid-19 in a country from the ECDC data source.

## Usage

```
estimate_infections(
data,
generation_time = gt_opts(),
delays = delay_opts(),
truncation = trunc_opts(),
rt = rt_opts(),
backcalc = backcalc_opts(),
gp = gp_opts(),
obs = obs_opts(),
stan = stan_opts(),
horizon = 7,
CrIs = c(0.2, 0.5, 0.9),
filter_leading_zeros = TRUE,
zero_threshold = Inf,
weigh_delay_priors = TRUE,
id = "estimate_infections",
verbose = interactive(),
reported_cases
)
```

## Arguments

- data
A

`<data.frame>`

of confirmed cases (confirm) by date (date).`confirm`

must be numeric and`date`

must be in date format.- generation_time
A call to

`gt_opts()`

(or its alias`generation_time_opts()`

) defining the generation time distribution used. For backwards compatibility a list of summary parameters can also be passed.- delays
A call to

`delay_opts()`

defining delay distributions and options. See the documentation of`delay_opts()`

and the examples below for details.- truncation
A call to

`trunc_opts()`

defining the truncation of the observed data. Defaults to`trunc_opts()`

, i.e. no truncation. See the`estimate_truncation()`

help file for an approach to estimating this from data where the`dist`

list element returned by`estimate_truncation()`

is used as the`truncation`

argument here, thereby propagating the uncertainty in the estimate.- rt
A list of options as generated by

`rt_opts()`

defining Rt estimation. Defaults to`rt_opts()`

. Set to`NULL`

to switch to using back calculation rather than generating infections using Rt.- backcalc
A list of options as generated by

`backcalc_opts()`

to define the back calculation. Defaults to`backcalc_opts()`

.- gp
A list of options as generated by

`gp_opts()`

to define the Gaussian process. Defaults to`gp_opts()`

. Set to`NULL`

to disable the Gaussian process.- obs
A list of options as generated by

`obs_opts()`

defining the observation model. Defaults to`obs_opts()`

.- stan
A list of stan options as generated by

`stan_opts()`

. Defaults to`stan_opts()`

. Can be used to override`data`

,`init`

, and`verbose`

settings if desired.- horizon
Numeric, defaults to 7. Number of days into the future to forecast.

- CrIs
Numeric vector of credible intervals to calculate.

- filter_leading_zeros
Logical, defaults to TRUE. Should zeros at the start of the time series be filtered out.

- zero_threshold
Numeric defaults to Inf. Indicates if detected zero cases are meaningful by using a threshold number of cases based on the 7-day average. If the average is above this threshold then the zero is replaced using

`fill`

.- weigh_delay_priors
Logical. If TRUE (default), all delay distribution priors will be weighted by the number of observation data points, in doing so approximately placing an independent prior at each time step and usually preventing the posteriors from shifting. If FALSE, no weight will be applied, i.e. delay distributions will be treated as a single parameters.

- id
A character string used to assign logging information on error. Used by

`regional_epinow()`

to assign errors to regions. Alter the default to run with error catching.- verbose
Logical, defaults to

`TRUE`

when used interactively and otherwise`FALSE`

. Should verbose debug progress messages be printed. Corresponds to the "DEBUG" level from`futile.logger`

. See`setup_logging`

for more detailed logging options.- reported_cases
Deprecated; use

`data`

instead.

## Value

A list of output including: posterior samples, summarised posterior samples, data used to fit the model, and the fit object itself.

## Examples

```
# \donttest{
# set number of cores to use
old_opts <- options()
options(mc.cores = ifelse(interactive(), 4, 1))
# get example case counts
reported_cases <- example_confirmed[1:60]
# set an example generation time. In practice this should use an estimate
# from the literature or be estimated from data
generation_time <- Gamma(
shape = Normal(1.3, 0.3),
rate = Normal(0.37, 0.09),
max = 14
)
# set an example incubation period. In practice this should use an estimate
# from the literature or be estimated from data
incubation_period <- LogNormal(
meanlog = Normal(1.6, 0.06),
sdlog = Normal(0.4, 0.07),
max = 14
)
# set an example reporting delay. In practice this should use an estimate
# from the literature or be estimated from data
reporting_delay <- LogNormal(mean = 2, sd = 1, max = 10)
# for more examples, see the "estimate_infections examples" vignette
def <- estimate_infections(reported_cases,
generation_time = gt_opts(generation_time),
delays = delay_opts(incubation_period + reporting_delay),
rt = rt_opts(prior = list(mean = 2, sd = 0.1)),
stan = stan_opts(control = list(adapt_delta = 0.95))
)
#> Warning: There were 15 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
# real time estimates
summary(def)
#> measure estimate
#> <char> <char>
#> 1: New infections per day 2280 (1042 -- 4985)
#> 2: Expected change in daily reports Likely decreasing
#> 3: Effective reproduction no. 0.89 (0.6 -- 1.3)
#> 4: Rate of growth -0.031 (-0.15 -- 0.085)
#> 5: Doubling/halving time (days) -23 (8.2 -- -4.7)
# summary plot
plot(def)
options(old_opts)
# }
```