Learning versus habit formation: Optimal timing of lockdown for disease containment

We analyze a model where the government has to decide whether to impose a lockdown in a country to prevent the spread of a possibly virulent disease. If the government decides to impose a lockdown, it has to determine its intensity, timing and duration. We find that there are two competing effects that push the decision in opposite directions. An early lockdown is beneficial not only to slow down the spread of the disease, but creates beneficial habit formation (such as social distancing, developing hygienic habits) that persists even after the lockdown is lifted. Against this benefit of an early lockdown, there is a cost from loss of information about the virulence and spread of the disease in the population in addition to a direct cost to the economy. Based on the prior probability of the disease being virulent, we characterize the timing, intensity and duration of a lockdown with the above mentioned trade offs. Specifically, we show that as the precision of learning goes up, a government tends to delay the imposition of lockdown. Conversely, if the habit formation parameter is very strong, a government is likely to impose an early lockdown.