  We consider the low-prevalence linearized SEIR epidemic model for a society
that has resolved to keep future infections low in anticipation of a vaccine.
The society can vary its amount of potentially-infection-spreading activity
over time, within a certain feasible range. Because the activity has social or
economic value, the society aims to maximize activity overall subject to
infection rate constraints. We find that consistent policies are the worst
possible in terms of activity, while the best policies alternate between high
and low activity. In a variant involving multiple subpopulations, we find that
the best policies are maximally coordinated (maintaining similar prevalence
among subpopulations) but oscillatory (having growth rates that vary in time).
It turns out that linearized SEIR is mathematically equivalent to an idealized
racecar model (with different subpopulations corresponding to different cars)
and the amount of fuel used corresponds to the amount of activity. Using this
analogy, steady V-shaped formations (in which one subpopulation "leads the way"
with consistently higher prevalence and activity, while others follow behind
with lower prevalence and activity) are especially problematic. These
formations are very effective at minimizing fuel use, hence very ineffective at
boosting activity. In an appendix, we obtain analogous results for alternative
notions of activity, which incorporate crowding effects.
