Could early quarantine of territories (States, provinces, countries) without infections be suboptimal?
Let's take the case of Argentinian Provinces with no known infections, and to a lesser extent, provinces with just one infection. Due to a national quarantine, these eleven provinces without cases and five provinces with one case are supposed to apply the same quarantine as the touristic and mercantile metropolis of Ciudad de Buenos Aires with 58 known infections.
To put the question into theoretical terms, we want to assign a utility value to starting the quarantine at different times: u(t), the utility function is a mix of health and economic variables. In order to simplify the question and avoid delving into the weighing of health vs economic utilities, assume that we also want to find the t or ts where the peak of simultaneous infections is the lowest, and that the utility will only be used as a tiebreaker between two options with an identical peak simultaneous infection.
Unless I'm missing something, the optimal moment to start a quarantine will be when the amount of known infections is higher than zero. Starting a quarantine with zero known infections will incur economic costs while not reducing peak simultaneous infections. Starting a quarantine with one known infection however, will only slightly lower peak simultaneous infections, but will delay the start of economic inactivity and thus increase the economic endurance of the territory.