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

Uncertainty is propagated from all inputs into the final parameterestimates, helping to mitigate spurious findings. This is handledinternally. The time-varying reproduction estimates and the uncertaingeneration time also give time-varying estimates of the rate ofgrowth.

{EpiNow2} provides three models:

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

• estimate_secondary(): Estimate the relationshipbetween 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 truncationdistribution from multiple snapshots of the same data source over time.For more flexibility, check out the{epinowcast}package.

The default model inestimate_infections() uses anon-stationary Gaussian process to estimate the time-varyingreproduction number and infer infections. Other options, which generallyreduce runtimes at the cost of the granularity of estimates or real-timeperformance, include:

• A stationary Gaussian process (faster to estimate but currentlygives reduced performance for real time estimates).
• User specified breakpoints.
• A fixed reproduction number.
• A piecewise constant, combining a fixed reproduction number withbreakpoints.
• A random walk, combining a fixed reproduction number with regularlyspaced 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 theforecast horizon.

By default, all these models are fit withMCMCsampling using therstanR package as the backend. Users can, however, switch to use approximatealgorithms likevariationalinference, thepathfinderalgorithm, orLaplaceapproximation especially for quick prototyping. The latter twomethods are provided through thecmdstanr Rpackage, so users will have to install that separately.

The documentation forestimate_infections providesexamples of the implementation of the different options available.

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

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

• regional_epinow(): Efficiently runepinow() across multiple regions in an efficientmanner.

These two functions callestimate_infections(), whichworks to reconstruct cases by date of infection from reported cases.

For more details on using each function corresponding functiondocumentation.

The Getting Started vignette (seevignette("EpiNow2"))is your quickest entry point to the package. It provides a quick runthrough of the two main functions in the package and how to set up themup. It also discusses how to summarise and visualise the results afterrunning the models.

More broadly, users can also learn the details of estimating delaydistributions, nowcasting, and forecasting in a structured way throughthe free and open short-course,“Nowcasting and forecastinginfectious disease dynamics”, developed by some authors of thispackage.

The package has two websites: one forthe stable release version onCRAN, and another forthe version indevelopment. These two provide various resources for learning aboutthe package, including the function reference, details about each model(model definition), workflows for each model (usage), and case studiesor literature of applications of the package. However, the developmentwebsite may contain experimental features and information not yetavailable in the stable release.

The workflow vignette (seevignette("estimate_infections_workflow")) provides guidanceon the end-to-end process of estimating reproduction numbers andperforming short-term forecasts for a disease spreading in a

In different vignettes we provide the mathematical definition of eachmodel. For example, the model definition vignette forestimate_infections() can be found invignette("estimate_infections").

A simple example of using the package to estimate a national Rt forCovid-19 can be foundhere.