Virus Dynamics with Behavioral Responses

Dasaratha, Krishna

Motivated by epidemics such as COVID-19, we study the spread of a contagious disease when people change their behavior to respond to the disease prevalence. We extend the SIR epidemiological model to include endogenous meeting rates. Individuals benefit from economic activity, but higher activity also leads to more interactions with potentially infected individuals. The main focus is a theoretical analysis of the contagion dynamics with a population of optimizing agents reacting myopically to the current disease prevalence. In the leading case, the infection prevalence is single-peaked. We obtain a simple condition for when several types of public-health interventions or changes in disease prevalence will paradoxically increase infection rates due to risk compensation. This condition implies that behavioral responses are most likely to undermine public-health interventions near the peak of severe diseases. We also derive an explicit formula for the behavior of a heterogeneous population. A key difference from the homogeneous case is that high-risk individuals may choose to temporarily stop all activity when they are likely to encounter infected low-risk individuals.