The 1927 SIR contagion model is the dynamical system for an infection that passes at a constant rate in random pairwise meetings. Our Behavioral SI* Model assumes that everyone has access to a constant elasticity of avoidance technology. We then derive the passing rate in fully solvable Nash equilibrium of the game where everyone optimizes. The resulting dynamics are log-linear, and incidence is log-linear in prevalence, with slope less than one.
The SI* models yields extreme predictions for major contagions, not realized. At breakout, the SI* models capture exponential growth. In our BSI* model, increasing avoidance behavior bends the curve, and induces herd immunity at lower prevalence but a later time.
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 BSI* formula.
The BSI* model captures mandated social distancing or lockdowns in downward shifts of the line in log-prevalance - log-incidence space.
Keppo, Juusi, et al. "The behavioral SIR model, with applications to the Swine Flu and COVID-19 pandemics." Virtual Macro Seminar. 2020.