Modeling in EpiSewer

This is a conceptual overview over the modeling functionality in EpiSewer. See vignette("model-definition") for a mathematical definition of the underlying generative model, and vignette("detailed-example") for an example vignette.

Modules

EpiSewer uses 5 different modules to describe the data generating process behind the wastewater measurements: infections, shedding, sewage, sampling, and measurements. There is a 6th module to specify forecast functionality. Each of these modules consists of a number of module components, as shown below.

The modules are defined using their corresponding module function, i.e. by calling model_infections(), model_shedding(), model_sewage(), model_sampling(), model_measurements(), or model_forecast().

Modeling functions

Components in a module can be specified using suitable modeling functions. There are 5 types of modeling functions:

• _observe: We provide observation data for this component. For example, we can use concentrations_observe() if we have observed concentration measurements and want to fit the model to them.
• _assume: We assume the values for this component. For example, we can use generation_dist_assume() to provide a generation time distribution from the literature.
• _calibrate: This is similar to _assume, but instead of directly specifying the value for an assumption, we calibrate it to some other assumption or data. For example, we can use load_per_case_calibrate() to calibrate the shedding load per case to case data (so that the estimated infections will roughly match the observed case numbers).
• _estimate: We estimate this component as a parameter of the model. For example, we can use noise_estimate() if we don’t know how much noise the measurements have and want to estimate this from the data.
• _none: We do not model this component. For example, we can use sample_effects_none() if we don’t want to model any sample effects on the measurements.

To find out which modeling functions are available for a given component, you can consult the documentation or use the helper component_functions():

EpiSewer::component_functions("infection_noise")
#> [1] "infection_noise_none()"     "infection_noise_estimate()"

💡 Multiple modeling options

Some components have multiple versions of the same modeling function type. For example, there are currently three approaches to estimate the reproduction number, namely R_estimate_splines() (smoothing splines), R_estimate_rw() (random walk), R_estimate_ets() (exponential smoothing), and R_estimate_approx() (approximation of renewal model).

EpiSewer::component_functions("R")
#> [1] "R_estimate_approx()"  "R_estimate_splines()" "R_estimate_rw()"     
#> [4] "R_estimate_ets()"

❗ Modeling restrictions

Not all components support all modeling types. For example, EpiSewer currently only offers generation_dist_assume(), but not generation_dist_estimate, generation_dist_calibrate, or generation_dist_observe.

EpiSewer::component_functions("generation_dist")
#> [1] "generation_dist_assume()"

This is because estimating the generation time distribution from data is not yet supported (but may be added in the future).

Data and assumptions

The sewer_data() and sewer_assumptions() functions are convenience functions that allow you to collect all observation data and modeling assumptions in one place. This can improve overview and allows to run EpiSewer under its default settings without repeating the component definitions:

ww_data <- sewer_data(
  measurements = SARS_CoV_2_Zurich$measurements,
  flows = SARS_CoV_2_Zurich$flows,
  cases = SARS_CoV_2_Zurich$cases # optional
  )

ww_assumptions <- sewer_assumptions(
  generation_dist = get_discrete_gamma_shifted(gamma_mean = 3, gamma_sd = 2.4),
  shedding_dist = get_discrete_gamma(gamma_shape = 0.929639, gamma_scale = 7.241397),
  shedding_reference = "symptom_onset",
  incubation_dist = get_discrete_gamma(gamma_shape = 8.5, gamma_scale = 0.4),
)

EpiSewer(
  data = ww_data,
  assumptions = ww_assumptions
)

What happens under the hood is that when individual model components are not provided with the data or assumptions they need, they search the data and assumption arguments passed to the EpiSewer() function.

💡 It is always possible to mix both approaches and specify data or assumptions explicitly in the model component:

# Leave out flows from the data
ww_data <- sewer_data(
  measurements = SARS_CoV_2_Zurich$measurements,
  #flows = SARS_CoV_2_Zurich$flows
  cases = SARS_CoV_2_Zurich$cases
)

# Leave out the generation time distribution
ww_assumptions <- sewer_assumptions(
  #generation_dist = get_discrete_gamma_shifted(gamma_mean = 3, gamma_sd = 2.4),
  shedding_dist = get_discrete_gamma(gamma_shape = 0.929639, gamma_scale = 7.241397),
  shedding_reference = "symptom_onset",
  incubation_dist = get_discrete_gamma(gamma_shape = 8.5, gamma_scale = 0.4),
)

# Provide flows directly to sewage module
ww_sewage <- model_sewage(
  flows = flows_observe(SARS_CoV_2_Zurich$flows)
)

# Provide generation time distribution directly to infections module
ww_infections <- model_infections(
  generation_dist = generation_dist_assume(
    get_discrete_gamma_shifted(gamma_mean = 3, gamma_sd = 2.4)
  )
)

# Combine everything
result <- EpiSewer(
  data = ww_data,
  assumptions = ww_assumptions,
  sewage = ww_sewage,
  infections = ww_infections
)

Note that if the same data or assumptions are supplied via the sewer_data()/sewer_assumptions() and the individual component, EpiSewer() will compare both arguments and throw an error if they differ.