EpiNow2: Estimate real-time case counts and time-varying epidemiological parameters

{EpiNow2} estimates the time-varying reproduction number on cases by date of infection (using a similar approach to that implemented in {EpiEstim}). True infections, treated as latent and unobserved, are estimated and then mapped to observed data (for example cases by date of report) via one or more delay distributions (in the examples in the package documentation these are an incubation period and a reporting delay) and a reporting model that can include weekly periodicity.

Uncertainty is propagated from all inputs into the final parameter estimates, helping to mitigate spurious findings. This is handled internally. The time-varying reproduction estimates and the uncertain generation time also give time-varying estimates of the rate of growth.

{EpiNow2} provides three models:

• estimate_infections(): Reconstruct cases by date of infection from reported cases.

• estimate_secondary(): Estimate the relationship between primary and secondary observations, for example, deaths (secondary) based on hospital admissions (primary), or bed occupancy (secondary) based on hospital admissions (primary).

• estimate_truncation(): Estimate a truncation distribution from multiple snapshots of the same data source over time. For more flexibility, check out the {epinowcast} package.

The default model in estimate_infections() uses a non-stationary Gaussian process to estimate the time-varying reproduction number and infer infections. Other options, which generally reduce runtimes at the cost of the granularity of estimates or real-time performance, include:

• A stationary Gaussian process (faster to estimate but currently gives reduced performance for real time estimates).
• User specified breakpoints.
• A fixed reproduction number.
• A piecewise constant, combining a fixed reproduction number with breakpoints.
• A random walk, combining a fixed reproduction number with regularly spaced breakpoints (i.e weekly).
• A deconvolution/back-calculation method for inferring infections, followed with calculating the time-varying reproduction number.
• Adjustment for the remaining susceptible population beyond the forecast horizon.

By default, all these models are fit with MCMC sampling using the rstan R package as the backend. Users can, however, switch to use approximate algorithms like variational inference, the pathfinder algorithm, or Laplace approximation especially for quick prototyping. The latter two methods are provided through the cmdstanr R package, so users will have to install that separately.

The documentation for estimate_infections provides examples of the implementation of the different options available.

{EpiNow2} is designed to be used via a single function call to two functions:

• epinow(): Estimate Rt and cases by date of infection and forecast these infections into the future.

• regional_epinow(): Efficiently run epinow() across multiple regions in an efficient manner.

These two functions call estimate_infections(), which works to reconstruct cases by date of infection from reported cases.

For more details on using each function corresponding function documentation.

The Getting Started vignette (see vignette("EpiNow2")) is your quickest entry point to the package. It provides a quick run through of the two main functions in the package and how to set up them up. It also discusses how to summarise and visualise the results after running the models.

More broadly, users can also learn the details of estimating delay distributions, nowcasting, and forecasting in a structured way through the free and open short-course, “Nowcasting and forecasting infectious disease dynamics”, developed by some authors of this package.

The package has two websites: one for the stable release version on CRAN, and another for the version in development. These two provide various resources for learning about the package, including the function reference, details about each model (model definition), workflows for each model (usage), and case studies or literature of applications of the package. However, the development website may contain experimental features and information not yet available in the stable release.

The workflow vignette (see vignette("estimate_infections_workflow")) provides guidance on the end-to-end process of estimating reproduction numbers and performing short-term forecasts for a disease spreading in a

In different vignettes we provide the mathematical definition of each model. For example, the model definition vignette for estimate_infections() can be found in vignette("estimate_infections").

A simple example of using the package to estimate a national Rt for Covid-19 can be found here.