Learning or habit formation? Optimal timing of lockdown for disease containment

We analyse 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 either direction. An early lockdown is beneficial not only to slow down the spread of the disease, but to create beneficial habit formation (such as social distancing, developing hygienic habits) that persists even after the lockdown is lifted. Against that, an early lockdown in addition to damaging the economy, leads to a loss of information and impedes learning about the nature and the dynamics of the disease. Based on the prior probability of the disease being virulent, we characterise the timing, intensity and duration of a lockdown with the above mentioned tradeoffs. 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.