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

2020-24 | July 13, 2020

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.

Article Citation

Lansing, Kevin J., Lily M. Seitelman, Nicolas Petrosky-Nadeau, Reuven Glick, and Shelby R. Buckman. 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 https://doi.org/10.24148/wp2020-24

About the Authors
Abstract image representing a seat vacancy.
Reuven Glick is a group vice president in the Economic Research Department of the Federal Reserve Bank of San Francisco. Learn more about Reuven Glick
Kevin Lansing
Kevin Lansing is a senior research advisor in the Economic Research Department of the Federal Reserve Bank of San Francisco. Learn more about Kevin Lansing
Nicolas Petrosky-Nadeau
Nicolas Petrosky-Nadeau is a vice president in the Economic Research Department of the Federal Reserve Bank of San Francisco. Learn more about Nicolas Petrosky-Nadeau