epyestim estimates the effective reproduction number from time series of reported case numbers of epidemics. It is a Python reimplementation of the method outlined by Huisman et al. [1], making use of the method by Cori et al. [2] to estimate the reproduction number R from infection data, available in the R package EpiEstim [3].

The main steps for estimation of the effective reproduction number are:

• Bootstrapping the series of reported case numbers
• Smoothing using a LOWESS filter
• MLE of the infection incidence time series using an adaptation of the Richardson-Lucy deconvolution algorithm.
• Bayesian estimation of the effective reproduction number using the method of Cori et al. [2]

Aggregate estimates for the reproduction number are obtained by bootstrap aggregation (bagging).

The user can choose to output either time-varying estimates or piecewise constant estimates on fixed arbitrary time intervals.

pip install epyestim

Basic usage of the epyestim package applied to COVID-19 data is explained in the Jupyter tutorial notebook.

The core functions relevant for users are:

• epyestim.bagging_r for the complete estimation process outlined above
• epyestim.covid19.r_covid for the same function with default parameters for COVID-19
• epyestim.estimate_r.estimate_r for the R estimation from infection numbers, based on the EpiEstim package

• Lorenz Hilfiker
• Johannes Josi

Error reports and suggestions for improvements via GitHub issues are very welcome.

[1] Jana S. Huisman, Jeremie Scire, Daniel Angst, Richard Neher, Sebastian Bonhoeffer, Tanja Stadler: A method to monitor the effective reproductive number of SARS-CoV-2 https://ibz-shiny.ethz.ch/covid-19-re/methods.pdf

[2] Anne Cori, Neil M. Ferguson, Christophe Fraser, Simon Cauchemez: A New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics, American Journal of Epidemiology, Volume 178, Issue 9, 1 November 2013, Pages 1505–1512, https://doi.org/10.1093/aje/kwt133

[3] EpiEstim CRAN package: https://cran.r-project.org/web/packages/EpiEstim/index.html