The Behavioral SIR Model, with Applications to the Swine Flu and COVID-19 Pandemics
Samuel P Engle, Jussi Keppo, Marianna Kudlyak, Elena Quercioli, Lones Smith, Andrea Wilson
Abstract: The 1927 SIR contagion model assumes an infection passes in random pairwise meetings, and derives a linear dynamical system. We propose and test a log-linear modification that reflects the Nash equilibrium of a costly avoidance game. In our Behavioral SIR Model (BSIR), the passing rate falls as a hyperbolic function of the prevalence, and therefore incidence is log-linear in prevalence. The SIR Model yields extreme predictions for major contagions, not realized, even without systemic social distancing or lockdowns. At breakout, the "curve bends" in the SIR model only with heterogeneous agents. In our BSIR model, increasing avoidance behavior bends the curve in the homogenous agent model. Also, herd immunity happens at lower prevalence in the BSIR Model. Our model is tractable, and better explains incidence data during the 2009 Swine Flu and the COVID-19 pandemic. In both cases, we statistically reject the SIR model. For Swine Flu, across states, the prevalence elasticity ranges from 0.8 to 0.9. We find a similar slope at breakout in the COVID-19 pandemic, and verify that its curve bending matches our BSIR formula. The same model --- with a similar slope but lower intercept --- but with increased losses explains data from national lockdowns for COVID-19.
Slides, Simon Mongey's COVID Search and Matching May 14 2020
Virtual macro seminar on April 10th (YouTube Link), Slides Apr 10 2020, Virtual Macro