Social multipliers and the Covid-19 epidemic: Analysis through constrained maximum entropy modeling

Social multipliers occur when individual actions influence other individual actions so as to lead to amplified aggregate effects. Epidemic infections offer a dramatic example of this phenomenon since individual actions such as social distancing and masking that have small effects on individuals’ risk can have very large effects in reducing risk when they are widely adopted. This paper uses the info-metric method of constrained maximum entropy modeling to estimate the impact of social multiplier effects in the Covid-19 epidemic with a model that infers the length of infection, the rate of mortality, the base infection factor, and reductions in the infection factor due to changes in social behavior from data on daily infections and deaths. When the model takes account of the rate of reporting of infections, it can produce three rather different scenarios of epidemic dynamics, which have marginally different posterior probabilities: one in which reporting is very low, under 10% and the estimated infection is correspondingly large, and immunity effects play a significant role in stabilizing the epidemic; a second in which reporting is on the order of 25% and the model estimates a significant portion of the population as having inherent immunity to the infection; and a third where reporting rates are close to 100%, and the epidemic is controlled mostly by changes in social behavior. These qualitatively different scenarios reflect the limited data the method can extract information from in this case.