  Motivated by epidemics such as COVID-19, we study the spread of a contagious
disease when behavior responds to the disease's prevalence. We extend the SIR
epidemiological model to include endogenous meeting rates. Individuals benefit
from economic activity, but activity involves interactions with potentially
infected individuals. The main focus is a theoretical analysis of contagion
dynamics and behavioral responses to changes in risk. We obtain a simple
condition for when public-health interventions or variants of a disease will
have paradoxical effects on infection rates due to risk compensation.
Behavioral responses are most likely to undermine public-health interventions
near the peak of severe diseases.
