Working Paper

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

Abstract: We fit a simple epidemiology model to daily data on the number of currently-infected cases of COVID-19 in China, Italy, the United States, and Brazil. These four countries can be viewed as representing different stages, from late to early, 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. Using the model-implied time series of Rt, we construct a smoothed version of the in-sample trajectory which is used to project the future evolution of Rt and the out-of-sample number of infected and closed cases (recovered or deceased). For the United States, the number of infected cases is projected to peak around July 19. For Brazil, the number of infected cases is projected to peak around July 24. 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 in recent months has helped to reduce the effective reproduction number and reduce the spread of COVID-19.

Keywords: Coronavirus; Reproduction number; Epidemics; SEIR Model; COVID-19;

JEL Classification: C63; I12;

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Bibliographic Information

Provider: Federal Reserve Bank of San Francisco

Part of Series: Working Paper Series

Publication Date: 2020-06-30

Number: 2020-24

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