  Within the context of SEIR models, we consider a lockdown that is both
imposed and lifted at an early stage of an epidemic. We show that, in these
models, although such a lockdown may delay deaths, it eventually does not avert
a significant number of fatalities. Therefore, in these models, the efficacy of
a lockdown cannot be gauged by simply comparing figures for the deaths at the
end of the lockdown with the projected figure for deaths by the same date
without the lockdown. We provide a simple but robust heuristic argument to
explain why this conclusion should generalize to more elaborate compartmental
models. We qualitatively discuss some important effects of a lockdown, which go
beyond the scope of simple models, but could cause it to increase or decrease
an epidemic's final toll. Given the significance of these effects in India, and
the limitations of currently available data, we conclude that simple
epidemiological models cannot be used to reliably quantify the impact of the
Indian lockdown on fatalities caused by the COVID-19 pandemic.
