Epidemic outbreaks and the optimal lockdown area: a spatial normative approach

Infectious diseases generate heterogeneous economic and health impacts within countries, thus it is essential to account for the spatial dimension in the design of epidemic management programs. We analyze the optimal regional policy to contain the spread of a communicable disease in a spatial framework with endogenous determination of the regional borders characterizing which policy regime will prevail. Specifically, the social planner needs to choose how to split the entire spatial economy in a number of regions in which a different combination of lockdown and treatment measures will be employed: in some region the only mitigation instrument will be treatment, while in some other treatment will be accompanied by a partial lockdown. We characterize the optimal solution both in an early and an advanced epidemic setting, showing that according to the circumstances it may be convenient either to partition the spatial economy in multiple regions with differentiated policies or to consider it a unique region subject to the same policy measure. Moreover, we show that from a normative perspective it is rather difficult to understand how to effectively determine the optimal size of a lockdown area (and thus of the lockdown intensity) since this critically depends on a number of factors, including the initial spatial distribution of disease prevalence, the amount of resources diverted from one region to the other, and the possible spatio-temporal evolution of the disease.