Incentives, lockdown, and testing: from Thucydides' analysis to the COVID-19 pandemic.

In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal-agent problem with moral hazard, à la Cvitanić et al. (Finance Stoch 22(1):1-37, 2018), while an epidemic is spreading according to dynamics given by compartmental stochastic SIS or SIR models, as proposed respectively by Gray et al.