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COVID-19: $R_0$ is lower where outbreak is larger

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  • Pietro Battiston
  • Simona Gamba

Abstract

We use daily data from Lombardy, the Italian region most affected by the COVID-19 outbreak, to calibrate a SIR model individually on each municipality. These are all covered by the same health system and, in the post-lockdown phase we focus on, all subject to the same social distancing regulations. We find that municipalities with a higher number of cases at the beginning of the period analyzed have a lower rate of diffusion, which cannot be imputed to herd immunity. In particular, there is a robust and strongly significant negative correlation between the estimated basic reproduction number ($R_0$) and the initial outbreak size, in contrast with the role of $R_0$ as a \emph{predictor} of outbreak size. We explore different possible explanations for this phenomenon and conclude that a higher number of cases causes changes of behavior, such as a more strict adoption of social distancing measures among the population, that reduce the spread. This result calls for a transparent, real-time distribution of detailed epidemiological data, as such data affects the behavior of populations in areas affected by the outbreak.

Suggested Citation

  • Pietro Battiston & Simona Gamba, 2020. "COVID-19: $R_0$ is lower where outbreak is larger," Papers 2004.07827, arXiv.org.
  • Handle: RePEc:arx:papers:2004.07827
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    1. Michael Greenstone & Vishan Nigam, 2020. "Does Social Distancing Matter?," Working Papers 2020-26, Becker Friedman Institute for Research In Economics.
    2. Richard A. Kronmal, 1993. "Spurious Correlation and the Fallacy of the Ratio Standard Revisited," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 156(3), pages 379-392, May.
    3. Andrew Atkeson, 2020. "How Deadly is COVID-19? Understanding the Difficulties with Estimation of its Fatality Rate," Staff Report 598, Federal Reserve Bank of Minneapolis.
    4. Callum Jones & Thomas Philippon & Venky Venkateswaran, 2021. "Optimal Mitigation Policies in a Pandemic: Social Distancing and Working from Home [A simple planning problem for covid-19 lockdown]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5188-5223.
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    Cited by:

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    2. Alexander Chudik & M. Hashem Pesaran & Alessandro Rebucci, 2023. "Social Distancing, Vaccination and Evolution of COVID-19 Transmission Rates in Europe," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 71(2), pages 474-508, June.
    3. Alexander Chudik & M. Hashem Pesaran & Alessandro Rebucci, 2021. "COVID-19 Time-Varying Reproduction Numbers Worldwide: An Empirical Analysis of Mandatory and Voluntary Social Distancing," Globalization Institute Working Papers 407, Federal Reserve Bank of Dallas.
    4. Wim Naudé & Ricardo Vinuesa, 2020. "Data, global development, and COVID-19: Lessons and consequences," WIDER Working Paper Series wp-2020-109, World Institute for Development Economic Research (UNU-WIDER).

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    More about this item

    JEL classification:

    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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