Replicating and projecting the path of COVID-19 with a model-implied reproduction number

Abstract

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 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 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.

How to go viral: A COVID-19 model with endogenously time-varying parameters

“…Our approach avoids such assumptions by decoupling the different phases of the pandemic through the various parameters. An alternative way to avoid such a tight relationship between different parts of the trajectory is to allow for time-varying parameters (e.g., Buckman et al (2020) for SIR models and Liu et al (2020) for statistical models). While such an approach provides great flexibility for fitting data, it may yield large forecast error bands if the parameters are allowed to vary without restriction.…”

“…A more common approach in the literature to estimate the effect of observables has been to estimate a TVP model with exogenous time variation, then to assess the correlation of the smoothed parameters with observables as a second step (e.g. Arroyo Marioli et al, 2020 , Buckman et al, 2020 , Dandekar and Barbastathis, 2020 ). Our approach estimates the effect of the observables jointly with the rest of the model, allowing for coherent quantification for both point estimates and posterior uncertainty.…”

“…Our reduced form approach seeks to minimize assumptions and gives the data a greater role in informing the researcher. A second approach is to estimate a SIR model with exogenous TVP (e.g., Arroyo Marioli et al, 2020 , Buckman et al, 2020 , Dandekar and Barbastathis, 2020 ), then check the correlation of the parameters with various observables, such as social distancing or quarantine measures, ex post. In contrast, we estimate the dependence of parameters on these predictors jointly with the rest of the model.…”

Assessment of Vaccination and Underreporting on COVID-19 Infections in Turkey Based On Effective Reproduction Number

“…In our model, we incorporated the daily R t values in order to account for the crowd behavior, such as using face coverings, social distancing or sheltering in place. Although this is not very common in mathematical models of epidemiology, Buckman et al [31], Kiamari et al [32] and Linka et al [33] utilize the effective reproduction number R t in their compartmental SIR models as where β is the contact rate and 1/ γ is the infectious period, [31, 33].…”

“…However, it would be more flexible and accurate to use a time dependent measure computed from the daily reported cases, namely effective reproduction number R t or R ( t ), to catch the dynamics of the disease [28, 29, 30]. Indeed, the transmission rate can be written in terms of the effective reproduction number as a time dependent function in some SIR models [31, 32, 33].…”