The effect of mobility reductions on infection growth is quadratic in many cases

Stay-at-home orders were introduced in many countries during the COVID-19 pandemic, limiting the time people spent outside their home and the attendance of gatherings. In this study, we argue from a theoretical model that in many cases the effect of such stay-at-home orders on incidence growth should be quadratic, and that this statement should also hold beyond COVID-19. That is, a reduction of the out-of-home duration to, say, 70% of its original value should reduce incidence growth and thus the effective R-value to 70%·70%=49% of its original value. We then show that this hypothesis can be substantiated from data acquired during the COVID-19 pandemic by using a multiple regression model to fit a combination of the quadratic out-of-home duration and temperature to the COVID-19 growth multiplier. We finally demonstrate that many other models, when brought to the same scale, give similar reductions of the effective R-value, but that none of these models extend plausibly to an out-of-home duration of zero.