Working Papers

2020-24 | July 2020


Replicating and Projecting the Path of COVID-19 with a Model-Implied Reproduction Number


We demonstrate a methodology for replicating and projecting the path of COVID-19 using a simple epidemiology model. We fit the model to daily data on the number of infected cases in China, Italy, the United States, and Brazil. These four countries can be viewed as representing different stages, from later to earlier, of a COVID-19 epidemic cycle. We solve for a model-implied effective reproduction number Rt each day so that the model closely replicates the daily number of currently infected cases in each country. For out-of-sample projections, we fit a behavioral function to the in-sample data that allows for the endogenous response of Rt to movements in the lagged number of infected cases. We show that declines in measures of population mobility tend to precede declines in the model-implied reproduction numbers for each country. This pattern suggests that mandatory and voluntary stay-at-home behavior and social distancing during the early stages of the epidemic worked to reduce the effective reproduction number and mitigate the spread of COVID-19.

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Article Citation

Buckman, Shelby R, Reuven Glick, Kevin J. Lansing, Nicolas Petrosky-Nadeau, and Lily M. Seitelman. 2020. "Replicating and Projecting the Path of COVID-19 with a Model-Implied Reproduction Number," Federal Reserve Bank of San Francisco Working Paper 2020-24. Available at